Aorist Inactive (Edit: Typo: Should be Infinitive) usually implies something that WILL take place, hence a sort of "future tense".
And you failed to show any objective link that discussed this "Absolute sense" you keep referring to, gramatically. Your definition seems to be purely a Theological presumption. As in, you are saying he spoke "Absolutely" because you are presuming it was Trinitarian.
And then of course, there's the issue that Ehyeh Asher Ehyeh means I WILL BE and not so much "I Am". If you're going to say I'm wrong on that, you'll be up against Theodotion, Aquila, and numerous Hebrew scholars who all agree that the Divine name revealed to Moses is not really "I am" but "I shall/will be". So please post a link defining this "Absolute sense". Just because many translate it as "I am" does not trump Aquila and Theodotion's translation. So you're then stuck with "I am" not even meaning the Divine name.
As anyone can see, here is "Genesthai" being used to define something that WILL be. Thus, if Yashua used a verb tense that usually means "will Become/to eventually be" in the Past tense, its an indicator that his use of "I am" was past tense too. I'll take Oxford Greek professor James Moffat's opinion on this matter over yours. Luke 9:36 and 3:22 are the only cases here where it would match the use in John 8:58, and for Yashua to make sense, his tense would have to have been in past tense. Every other example on this list uses the "To become/to eventually be" form.
Greek Concordance: ???????? (genesthai) -- 37 Occurrences
Matthew 20:26 V-ANM
BIB: ὑμῖν μέγας
γενέσθαι ἔσται ὑμῶν
NAS: wishes to become great
KJV: whosoever will be great among
INT: you great become let him be your
Matthew 24:6 V-ANM
BIB: Δεῖ γὰρ
γενέσθαι ἀλλ' οὔπω
NAS: for [those things] must take place, but [that] is not yet
KJV: [these things] must come to pass, but
INT: it is necessary indeed to take place but not yet
Matthew 26:54 V-ANM
BIB: οὕτως δεῖ
γενέσθαι
NAS: [which say] that it must happen this way?
KJV: thus it must be?
INT: thus it must be
Mark 1:17 V-ANM
BIB: ποιήσω ὑμᾶς
γενέσθαι ἁλιεῖς ἀνθρώπων
NAS: Me, and I will make you become fishers
KJV: you to become fishers
INT: I will make you to become fishers of men
Mark 10:43 V-ANM
BIB: θέλῃ μέγας
γενέσθαι ἐν ὑμῖν
NAS: wishes to become great
KJV: whosoever will be great among
INT: desires great to become among you
Mark 13:7 V-ANM
BIB: θροεῖσθε δεῖ
γενέσθαι ἀλλ' οὔπω
NAS: [those things] must take place; but [that is] not yet
KJV: [such things] must needs be; but
INT: be disturbed it must come to pass but not yet [is]
Luke 3:22 V-ANM
BIB: ἐξ οὐρανοῦ
γενέσθαι Σὺ εἶ
NAS: and a voice came out of heaven,
KJV: and a voice came from heaven,
INT: out of heaven came You are
Luke 9:36 V-ANM
BIB: ἐν τῷ
γενέσθαι τὴν φωνὴν
NAS: the voice had spoken, Jesus
INT: as occurred the voice
Luke 21:9 V-ANM
BIB: γὰρ ταῦτα
γενέσθαι πρῶτον ἀλλ'
NAS: must take place first,
KJV: must first come to pass; but the end
INT: for these things take place first but
Luke 23:24 V-ANM
BIB: Πιλᾶτος ἐπέκρινεν
γενέσθαι τὸ αἴτημα
NAS: that their demand be granted.
KJV: gave sentence that it should be as they
INT: Pilate ajudged to be done the demand
John 1:12 V-ANM
BIB: τέκνα θεοῦ
γενέσθαι τοῖς πιστεύουσιν
NAS: the right to become children
KJV: power to become the sons
INT: children of God to be to those that believe
John 3:9 V-ANM
BIB: δύναται ταῦτα
γενέσθαι
KJV: can these things be?
INT: can these things be
John 5:6 V-ANM
BIB: Θέλεις ὑγιὴς
γενέσθαι
NAS: to him, Do you wish to get well?
KJV: unto him, Wilt thou be made whole?
INT: Desire you well to become