Robby's question,
How long do you wait until you conclude that the experiment has failed to reveal the existence of God?
is merely the expression of impatience. The requirement of patience is not unique to religious propositions. In general it is impossible to know in advance that a strictly algorithmic process will terminate on a given input. This is known as the Halting Problem of computer science and it is practically ubiquitous in all scientific fields. This is a hard science and the proof is irrefutable.
The proposition that a given program will terminate on a given input is also in general falsifiable, but that does not prevent it from being verifiable.
To answer his objections point by point:
Lack of specific criteria: The skeptic's prayer is sufficiently specific. Knowing God or knowing that He exists is a very concrete and undeniable condition, no less so than verifying that your neighbor exists by knocking his door and seeing him or talking to him on the telephone. The only possible reason to argue otherwise is special pleading because the subject is God. We do not apply this criterion to any other proposition or thing, only God.
Absence of Scientific Methodology: Failure is that you know with certainty that there is no God (not because you failed to endure in performing the experiment properly or didn't really want to know). Success is that you know with certainty that there is a God. The existence of quarks can be (and has been) proven in similar manner.
Rejection of Specificity as "Unfair Restrictions": Is this not a self-imposed limitation? Of course if we are only guessing at how to approach God, the problem may appear intractable. On the other hand, if God sets the terms, for example, saying, "read this book, pray about it in faith and I'll tell you it is true", then that dispenses with any purported need for the experimenter to impose "unfair restrictions" on God and simultaneously eliminates objections 1 and 2.
Ambiguity in Recognizing God's Revelation: Does anyone know anything for certain? Philosophers debate this. There is identical propensity for supposed "ambiguity" in interpreting any scientific result. If we ask whether God exists, or whether His revelations are true, and we know that He has answered yes, no ambiguity remains. Therefore the question should be reverted to those professing to be scientists. Do they believe they can know anything for absolute certain? If not, the problem is their own doubtfulness. This strikes at the core of epistemology. Either a person can perceive and know something with certainty, or he cannot. If he can, again, there is no problem with the scientific proposition that we can know that God exists.
Failure to Exclude Alternative Hypotheses: The answer to Objection 4 eliminates this. If a person knows something is true he knows it. If you know that 2+2=4 this necessarily precludes "alternative hypotheses". Find someone who debates this, and I will show you someone who is not mentally fit or well. A person who tells you that your neighbor whom you have seen and conversed with does not exist or that you do not or cannot know that he really exists is merely gaslighting you. You know what you know and you do not need anyone else's permission or consensus to know it.
Skepticism as a Positive Sign: True religion welcomes verification, as does all true science, but you have to do your homework first. Peeking at the answer key to pass a test without putting in the effort to learn is a non-starter.
Overall Ineffectiveness of the Skeptic's Prayer as a Definitive Experiment: If the skeptic's prayer isn't it, then what is? It is totally appropriate and adequate to the task, as God Himself invites those who lack wisdom to ask Him for it, and He promises to give it to them. This is an exact framing of an invitation and experimental procedure along with the verification in completely scientific terms. What bothers Robby is that it requires patience and faith. But so does science.
So I would answer that Robby himself doesn't actually believe in (let alone understand) science.
Try to find a canonical definition of the Scientific Method anywhere that does not ultimately depend on both faith and patience. You cannot do it because it does not exist. There never was a scientific discovery that did not require both patience and faith. Is science therefore unscientific?
Can we legitimately categorize the Skeptic's Prayer as a "scientific experiment"?
Yes, absolutely, it satisfies exactly all of the rigorous criteria of a scientific experiment. The only way to debate this is to contend that there is no such thing as certain knowledge, but then there goes science out the window the moment one advances such an argument.
The "Scientific Method" without patience and faith is a pure hoax. The only way to prove that 2+2=4 or that quarks exist is to work it out until you have received a pure and undeniable witness of its truth. Once you do know it, it is fruitless to try to un-know it, and it does preclude alternative hypotheses (that's what knowledge does inherently).
Reason is merely plumbing.
As we say in my field of data science and deep learning, "garbage in, garbage out".
But if you put good stuff in you can get good stuff out. If you start with knowledge you can gain more knowledge. If you start with doubt you can multiply your doubts. If you begin with faith you can gain more faith. If you sow unbelief you can produce more shoddy reasons for unbelief.
The sowing and reaping of increasing amounts of unbelief does absolutely nothing to falsify the testimonies of millions who sow knowledge to gain more knowledge, and who exercise their faith and receive a reward of increased faith.