Many honest people who know Greek can explain it easily without having to force the ego eimi with God's name in the burning bush passage, and we don't have to be a Jahovah's Witness for this belief. Ouk Ego Eimi Jahovah's Witness (I am not a JW).
which on the surface, seems to be a direct reference to the way God revealed himself to Moses at the burning bush
Your question hinges on a number of presuppositions and ignorance of the original language. The main reason behind relating the two "I am" claims is by comparing two English translations, and concluding that somehow "I am" means God's name, even though that is not what the divine name YHWH means. The "I am" of Exodus 3:14 is actually in Greek LXX ὁ ὢν ἀπέσταλκέν με πρὸς ὑμᾶς. This "ho on" means "The Being" or "who is", as it is translated in LXX Brenton as, "And God spoke to Moses, saying, I am THE BEING; and he said, Thus shall ye say to the children of Israel, THE BEING has sent me to you." This ho own refers to the omnipresent actual name of God, that is ascribed to Jesus a number of times in book of Revelations, e.g. 1:8 Ἐγώ εἰμι τὸ Ἄλφα καὶ τὸ Ὦ, λέγει κύριος ὁ θεός, ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος, ὁ παντοκράτωρ. “I am the Alpha and the Omega,” says the Lord God, “who is and who was and who is to come, the Almighty.” Also, to Jesus in Rom 9:5, and to the father in 2Cor 11:31
The phrase "I am" is never a code for God's name or for anything unique or enigmatic, it means the same thing in English as it refers to in the Bible. Thus, ho on is more likely to be used as God's name, as it is literally his actual name, rather than the self-referent verb phrase. Wikipedia states on the ego eimi tradition under Other views:
This assumption is questioned by those who point out that in the Septuagint and in Philo's Life of Moses Greek ho on "the being", not ego eimi "I am", carries the greater part of the meaning.[12][13] Also that ho on "who is" occurs in Revelation 1:4,8 4:8, 11:17, 16:5.
A great analogy to explain the semantic fallacy of comparing two similar looking phrases in a common translation would be to equate 1Cor 15:10 Paul's claim "I am who I am because of God’s grace"(Voice), to God's name in Exodus 3:14, or by mistranslating it as "I AM WHO I AM", when the original language shows no similarity between the two. A proper and honest exegesis shows neither Paul nor Jesus, were claiming to be God in any of those phrases. Of, course, the implication of various Jesus' claims were Messianic, thus, indirectly divine claims, however, none of those are direct and explicit YHWH name in any case. Thus, we need to interpret the text beyond the surface, and not fall for any fallacy by quick jumping to conclusions without evidence.
As such, it would seem logical for the Jews to want to stone Jesus for (in their eyes) blasphemy ....
how can it be logically maintained that Jesus was not referencing the name (or title, or description - that particular distinction should be irrelevant) of God as revealed to Moses at the burning bush and applying it to himself?
A proper exegesis reveals that the logic for the blasphemy charge was his Messiah claims, that is what the agenda of John's narrative. The "I am the one" unique phrases in John refers to his identification with the expected Messiah. His Messianic claims were worthy of blasphemy to those who rejected him (John 5:18, 10:33), he was making himself "equal to God", by claiming to be the (divine) Messiah. In this context of John 8, where he claimed to be older than Abraham, it was an explicit Messiah claim. There is only one being who is greater than the patriarchs, above all, that is the Messiah, and he was considered equal to God.
Some Pre-New Testament Jewish commentaries on the Messiah found in the Jewish records:
Targum Jonathan ( 4th Century ) gives the introduction on Isa. 52:13:”Behold, my servant the Messiah shall prosper; he shall be high and increase and be exceedingly strong…“
Gersonides (1288-1344) on Deut. 18:18:
“In fact Messiah is such a prophet, as it is stated in the Midrasch on the verse,’Behold, my servant shall prosper…’ (Isa. 52:13).”
Midrash Tanchuma:
“He was more exalted than Abraham, more extolled than Moses, higher than the archangels” (Isa.52:13).
In the Midrash Tanhuma, parasha Toldot, it says:
“Who art thou, O great mountain?” (Zechariah 4:7) This refers to the King Messiah . And why does he call him the “great mountain?” Because he is greater than the patriarchs, as it is said, ” My servant shall be high, and lifted up, and lofty exceedingly .” He will be higher than Abraham who said, “I raise high my hand unto the Lord” (Gen. 14:22), lifted up above Moses, to whom it is said, “Lift it up into thy bosom” (Numbers 11:12), loftier than the ministering angels, of whom it is written, “Their wheels were lofty and terrible” (Ezekiel 1:18). And out of whom does he come forth? Out of David.
Yalkut ii: 571 (13th c.) says:
Who art thou, O great mountain (Zech. iv. 7.) This refers to the King Messiah . And why does he call him “the great mountain?” Because he is greater than the patriarchs, as it is said, ” My servant shall be high, and lifted up, and lofty exceedingly” — he will be higher than Abraham, . . . lifted up above Moses, . . . loftier than the ministering angels.
To suggest that these Messianic commentaries among the anti-Messianic Jews have been created after Jesus would be laughable, just as the "I AM" mistranslations or interpretations in John's Gospel. We should be careful in our interpretation by not blindly following any tradition of men driven by emotions.