I will focus on the difference between the account in John's Gospel and that in the Synoptics. I will start with two assumptions:
John had the text of the Synoptics available before him when composing his Gospel, so that when he deviated from the Synoptics' account he did it on purpose and for a purpose, which was providing not just factual accuracy (which he actually provided) but important theological meaning.
John's intention was that his Gospel be read in conjunction with the Synoptics, not to replace them.
That said, to apprehend the theological meaning of the account of Jesus' arrest in John's Gospel we need to take into account three data items:
First, the isolated statement "I Am" (Ego Eimi), with which Jesus identifies Himself twice in the passage, appears in 4 previous verses in John's Gospel:
«for unless you believe that I Am, you will die in your sins.» (Jn 8:24)
«When you have lifted up the Son of Man, then you will know that I Am, and that I do nothing on my own;» (Jn 8:28)
«Truly, truly, I say to you, before Abraham was, I Am.» (Jn 8:58)
«I am telling you now before it happens, so that when it comes to pass, you may believe that I Am.» (Jn 13:19)
In all these verses it is clear that Jesus applies to Himself the proper Name of God in the first person revealed in Ex 3:14: Ehyeh, "I Am". This is particularly evident in the first, second and fourth verses, in which Jesus notes the importance of {believing/knowing} that "He Is", echoing Isaiah 43:10 y 48:12.
Second. The Greek term "fell" (epesan) is used 5 times by the Apostle John in Revelation in the sense of "fall on their face" to worship: 5:8, 5:14, 7:11, 11:16 and 19:4.
Third. By the time of Jesus, the proper Name of God in the third person revealed in Ex 3:15: YHWH, "He causes to be" if vocalized YaHWeH, was uttered by only one person, the High Priest, on only one day of the year, the feast of Atonement (Yom Kippur), 6 times when making a sacrifice for his own sins, one time when drawing the lot for the he-goats, and 3 times when loading the iniquities and transgressions of the sons of Israel on the he-goat to be sent to the desert (Lev 16:20-22). The prayer used by the High Priest for the latter function, and the people's response, are in the Mishna, tractate Yoma, chapter 6:
He then came to the he-goat which was to be sent away to
Azazeil and forcefully leans his hands on it and confesses. And so he
would say: Please O YHWH, they have done wrong they have transgressed
they have sinned before You - Your nation the House of Israel, Please,
O YHWH, forgive them for their doing wrong, for their transgressions
and for their sins, as is written in the Torah of Moshe Your servant:
“For on this day He will effect atonement for you to purify you before
YHWH” (Leviticus 16:30). And when the priests and the people who were
standing in the courtyard heard the fully pronunced Name come from the
mouth of the High Priest they would kneel, prostate themselves, fall
on their faces, and call out: Blessed be the Name of His glorious
kingdom for ever and ever. He gave it over to the one who was to lead
it [to Azazeil].
http://www.emishnah.com/moed2/Yoma/6.pdf
http://www.sefaria.org/Mishnah_Yoma.6
From these data, the meaning of the fall to the ground of the party that had come to apprehend Jesus when He said "I Am" for the first time is crystal clear: Jesus is the High Priest who is carrying out the true Atonement prefigured by the rite in the Mosaic Law, and that at the time of loading the iniquities and transgressions of men on the victim that will carry them, pronunces the proper Name of God, with the difference, with respect to an ordinary High Priest, that:
since Jesus Himself is the victim, He bears and carries our iniquities and transgressions Himself,
since Jesus Himself is God, He pronounces the proper Name of God in the first person.
Finally, the third time when Jesus pronounces the proper Name of God in the first person as true High Priest of the true Atonement is not recorded in John's Gospel but in Mark's, in the reply to the High Priest
Again the high priest was questioning Him, and says to Him, "Are You
the Christ, the Son of the Blessed One?" And Jesus said, "I Am. And
you will see the Son of Man sitting at the right hand of Power and
coming with the clouds of heaven." (Mk 14:61-62)
To validate the interpretation of this "I Am" as the third uttering of the divine Name in the first person by Jesus as High Priest of the true Atonement, we must note that, in the Jewish rite, immediately after the High Priest finished his prayer uttering the divine Name by a third time, the goat was taken to the desert. Similarly, immediately after pronouncing the third "I Am" in Mk 14:62, Jesus started to be spit, striken, mocked and slapped by the Jews (Mk 14:65).
Acknowledgment: I learned of this theological meaning of the passage from a site on the revealed Name of God by a Jewish scholar:
http://www.exodus-314.com/home/introduction/exodus-314-in-christianity.html?id=39