Pulpit Commentary
Your BibleHub link missed the Pulpit Commentary which treats verse 32 together with verse 31. While the Pulpit Commentary editor is Anglican, I think the answer is applicable to the Reformed tradition as well.
After relating a possible historical background of the war simile (which Jesus may have used) and relating a modern version with Swiss contemplating war against France, the interpretation is as follows:
The first of these two little similes rather points to the building up of the Christian life in the heart and life. The second is an image of the warfare which' every Christian man must wage against the world, its passions, and its lusts. If we cannot brace ourselves up to the' sacrifice necessary for the completion of the building up of the life we know the Master loves; if we shrink from the cost involved in the warfare against sin and evil - a warfare which will only end with life - better for us not to begin the building or risk the war. It will be a wretched alternative, but still it will be best for us to make our submission at once to the world and its prince; at least, by so doing we shall avoid the scandal and the shame of injuring a cause which we adopted only to forsake.
My paraphrase of the commentary
As we contemplate whether to follow Jesus or not, the decision has to be all or nothing. Halfway only causes embarrassment to those who decide to choose all (choosing all means to potentially suffer and die as disciple while warring against the devil). In other words, if you can only do halfway, you shouldn't be a disciple. Of course, choosing nothing means making peace with the devil, which is a "wretched" alternative.
Calculating the cost here means weighing our options: do we want to suffer as disciple of Jesus but with eternal life as a reward, or do we want to be comfortable in the world but with eternal damnation as punishment? Jesus presents the only two honorable options. Don't go halfway and bring bad name to other Jesus's followers by trying to be saints but quit in the middle.
The Pulpit commentary on Luke 14:28-30 about the builder made a similar point:
So in the spiritual life, the would-be professor finds such living harder than he supposed, and so gives up trying after the nobler way of living altogether; and the world, who watched his feeble efforts and listened with an incredulous smile when he proclaimed his intentions, now ridicules him, and pours scorn upon what it considers an unattainable ideal. Such an attempt and failure injure the cause of God.
Non Reformed Interpretations
The OP disagrees with this interpretation, saying that the other King with 20,000 troops represents God, so making peace to the OP means completely different:
"don't start following Jesus if you are not confident, but negotiate with Him", and sooner rather than later, when He is still far away, rather than when He is near, and notices you don't have wedding garments, or oil for your lamp, or faith.
I cannot find support for that interpretation from a Reformed source. However, I did find a 1908 Catholic commentary on Luke mentioning how St. Gregory (unlike St. Cyril) thinks that the double army King is Christ:
But S. Gregory (Hom. 37) gives another interpretation. “The king that is about to come against us is Christ, who will come with a double army against a single one. For while we are scarcely prepared in deeds only, He will discomfit us at once, both in thought and deed. Let us send Him therefore an embassy; our tears, our works of mercy, and propitiatory victim.”
I also find a very interesting research article on this parable from the 2nd Temple perspective, with focus on the Hebrew idioms current at the time, plus a redaction theory of how the parable came to the final version in Luke. (Warning: the website's project is not Christian, it's an attempt to uncover the Hebraism within the Synoptic gospels. See rebuttal in the next section below.).
One of the 2 goals of the article is to precisely address the question:
What is the meaning of ἐρωτᾷ εἰς εἰρήνην (“he asks for peace”) in the King Going to War simile (Luke 14:32; L18)?
Their conclusion is:
It therefore appears that the original meaning of Jesus’ simile was not that the weaker king negotiated terms of peace, but that his submission to his stronger adversary was expressed in offering a humble salutation. Luke preserved this Hebraism which he found in his pre-synoptic source, but its meaning was not understood by later copyists of Luke’s Gospel. They therefore attempted to make Luke’s sentence intelligible by improving the Greek, which accounts for the variant readings in New Testament manuscripts.
We believe that the Tower Builder and King Going to War similes are an attempt to explain why full-time discipleship is not suitable for everyone. Not everyone had the freedom and the ability to give up their livelihoods and leave their families in order to travel with Jesus from place to place, obligations that were incumbent upon Jesus’ full-time disciples. We believe that these historical circumstances must be recognized in order to appreciate Jesus’ teaching on this issue.
Jesus did not equate becoming a full-time disciple with salvation, nor did he regard non-disciples as hostile to his mission or exclude them from the benefits of his ministry. To the contrary, Jesus recognized that for the vast majority of people it was better that they enjoy his words and deeds as observers and beneficiaries and that they put his teachings into practice in their daily lives—like the crowds who listened to Jesus’ teachings and who held him in high regard—than to leave their homes and communities in order to become full-time disciples with absolute commitments and obligations to Jesus’ mission. Full-time discipleship was for the select few who could set aside their ordinary activities and engagements for a time in order to master Jesus’ message in order that they, in turn, might accurately pass it on to others.
In the Tower Builder and King Going to War similes it is not the willingness or the desire of the men to set about their tasks, but their ability to successfully execute their intentions. Similarly, we believe that the situation the similes address does not pertain to the sympathy of would-be disciples to Jesus’ message, but to their ability to do their job well. Jesus was willing to take on as disciples only those whom he believed were up to the task.
Personal assessment from the Reformed tradition
As we can see from the above, this parable has been interpreted in many different ways corresponding to one's faith tradition / principles of interpretation. Unfortunately I couldn't find a clear & certifiably Reformed interpretation for the "peace" that the OP wants to interpret.
The 2nd Temple research article is definitely not suitable for Reformed consumption because the Jerusalem school hypothesis has received decisive rebuttal and "discommendation" (his word) in a very well researched and well written 1992 article by Michael L. Brown, an expert in Near Eastern languages and a conservative Bible college faculty member. The article points out how the Jerusalem School project turns out to advance a theory that the Greek canonized gospels we possess today are corrupted in such a way that they can no longer be considered inspired. The article discussed at length how the project has deep flaws in their assumptions as well as their bias in NOT presenting a more likely theory based on the widespread use of Septuagint in the time that the gospels were written. So by extension, their interpretation of the simile should be discarded from the Reformed perspective.
As a side note, I highly recommend studying Michael Brown's 1992 article (pdf version here) in depth to arm believers with critical thinking against the rising tide of attempts (some very subtle) to discredit the trustworthiness of the gospels in the form that we possess today. This includes other past attempts like the Jesus Seminar or the still influential Bart Ehrman project. All conservative Christians from all denominations believe that the gospels present faithfully the teaching of Jesus, despite some difficulties in understanding some of the parables.
Reformed tradition is strongly saying that God will provide everything an elect's need for salvation and that the elect is supposed to receive everything with gratitude. At the same time, the elect has to work hard to discern and defeat any temptation to sin with the grace that God will faithfully provide continuously until we enter heaven. The elect has to be a disciple, there is no choice. As long as the elect sides with God by completely trusting Jesus and receiving all grace with gratitude, there is no bargaining for peace needed. Therefore, it is unlikely that the 20,000 troops King represents God, and to me the Pulpit commentary is quite congruent with the Reformed overall theology. Therefore, the king with 20,000 troops represents the king of the world, the Devil, and the elect has to engage war with the Devil, with God's help of course.
The Reformed tradition moral lesson is thus: we cannot win against the Devil on our own, we need Jesus to save us. And please don't embarrass the cause by going halfway because it will damage the "brand".
Then the "halfway believer", the farmer who started the tower or the king who initiated the war but who quit in the middle probably represents someone who isn't one of the elect because God doesn't give him/her the grace to persevere to the end (the "P" in TULIP) while the elect will be able to win against the devil (even if the elect has to die prematurely) and receive the eternal inheritance.
