Okay, I’ll take the Apostolic Constitutions passage as a starting-point. (This post has already become super long, so I may try to get to the other things you mentioned in a follow-up.)
This reads καὶ τοῦτο ὑμῖν ἔστω νόμιμον αἰώνιον ἕως τῆς συντελείας τοῦ αἰῶνος, μέχρις ἂν ἔλθῃ ὁ Κύριος.
In context, what this is saying is that the command for Eucharistic memorial/sacrifice (Luke 22:19) is an ordinance that’s to be observed permanently, a νόμιμος αἰώνιος; and it’s described here as “permanent” precisely because it’s designed to cover the maximum amount of time possible from its present going forward. Of course, here, it does have a potential end in mind: when the Second Coming actually takes place, at the end of time. (Though obviously here we are nearly 2,000 years later, still waiting for this; and for all we know it could never happen.)
Interestingly though, just a couple of lines later, we also have another use of αἰώνιος: that faith in Christ yields ἀθάνατος ζωὴ καὶ αἰώνιος, “life that is immortal, everlasting.” This is clear appositional synonymy, where two adjectives are used together to mean the same thing.
But I wanna get back to νόμιμος αἰώνιος briefly. This phrase has its origin in the Hebrew Bible, where it’s used to describe various ordinances in the Torah like Leviticus 6:18; 10:9, where חק־עולם לדרתיכם is translated as νόμιμον αἰώνιον εἰς τὰς γενεὰς ὑμῶν (see also Leviticus 3:17, νόμιμον εἰς τὸν αἰῶνα εἰς τὰς γενεὰς ὑμῶν). Here, the permanence of the statute(s) is followed by a clause that seems to orient this span of time particularly toward the longevity of the Israelites’ descendants – which may be taken as loosely analogous to what we found in the Apostolic Constitutions. (See also Exodus 12:14 for an even closer parallel.)
But in line with some of the other things I’ve suggested, the idea here in Leviticus is almost certainly not just that this applies permanently throughout all the time the lineage continues, as if it foresaw some actual finite end to the lineage, but rather “permanently – that is, throughout all the time that it’s possible for the lineage to continue.” (The collocation of various uses of -לדר as in לדרתם or לדרתיכם, which are then followed by a noun modified by עולם, is suggestive here. See more on this below, e.g. in the section that mentions “close apposition of εἰς τὸν αἰῶνα and εἰς τὰς γενεὰς ὑμῶν.”)
This gains additional support from how elsewhere in the Hebrew Bible/Septuagint, in phrases similar to לדרתיכם/εἰς τὰς γενεὰς ὑμῶν, the pronoun at the end is dropped (Genesis 9:12?), and thus what we might more literally gloss as “throughout [all] generations” is no longer attached to anything more specific like “your generations,” “their generations,” etc. In these instances, “throughout [all] generations” clearly becomes synonymous with εἰς τὸν αἰῶνα, attaining the simple meaning “forever” and “permanently.”
For that matter, interestingly, Philo of Alexandria, at Ebr. 141, interpreting Leviticus 10:9, glosses the substantive νόμιμος αἰώνιος, “permanent/everlasting ordinance,” as νόμος ἀθάνατος, “immortal law” – incidentally, using the same word for “immortal” here as in the Apostolic Constitutions passage.
Another instructive example is Leviticus 3:17, where חקת עולם לדרתיכם is glossed as νόμιμον εἰς τὸν αἰῶνα εἰς τὰς γενεὰς ὑμῶν. What’s interesting here is that adjectival עולם (which in context we would otherwise translate as αἰώνιος) is glossed as adverbial εἰς τὸν αἰῶνα, creating a close apposition of εἰς τὸν αἰῶνα and εἰς τὰς γενεὰς ὑμῶν. (See also Exodus 40:15, עולם לדרתם/εἰς τὸν αἰῶνα εἰς τὰς γενεὰς αὐτῶν.) Again though, there are instances where the pronominal suffix/modifier in phrases like לדרתיכם/εἰς τὰς γενεὰς ὑμῶν is dropped where we might otherwise expect it, like in Genesis 9:12. (Actually לדרת עולם/εἰς γενεὰς αἰωνίους here.)
In terms of this phrase without any pronominal suffix, LXX Isaiah 51:8 is a particularly instructive example – where צדקתי לעולם תהיה וישועתי לדור דורים is translated ἡ δικαιοσύνη μου εἰς τὸν αἰῶνα ἔσται, τὸ δὲ σωτήριόν μου εἰς γενεὰς γενεῶν. Here we have a perfect apposition/doublet, where God’s righteousness lasts forever (εἰς τὸν αἰῶνα), and his salvation forever (εἰς γενεὰς γενεῶν), too. (See also two verses prior to this, וישועתי לעולם תהיה וצדקתי לא תחת.)
To err is human, so we all make mistakes, such as the spelling errors you refer to above. For example at the following url, is that you speaking of aionios occurring in Lev.25:46 & Exo.21:6:
You’re certainly correct. Rereading what I wrote, I gave the mistaken impression that instead of adverbial εἰς τὸν αἰῶνα in Leviticus 25:46 and Exodus 21:6, we have adjectival αἰώνιος.
Of course, my point isn’t that people’s arguments are invalidated by innocent mistakes like accidentally writing αἰώνιος for αἰών (or, as I did, referring to αἰώνιος instead εἰς τὸν αἰῶνα in alluding to those Torah passages). Rather, I criticize people who don’t even have the knowledge to recognize that there’s a huge difference between αἰών and αἰώνιος in the first place – not that they simply mistakenly misread one for the other, but that they don’t recognize the difference to begin with. (Incidentally, that’s precisely what seems to be happening in a discussion in the comment section of another post that I’m currently taking part in. See here: https://blogs.ancientfaith.com/orthodoxyandheterodoxy/2018/05/08/david-bentley-harts-the-new-testament-a-review/.)
On one last note though, you wrote
What i’ve found useful there are various references to aionios which have been shamefully omitted by the hell biased lexicons that are popular amongst the very large body of the pro eternal hell book buyers club. Which means they’ll be buying a lot of those lexicons. Cha ching.
There is no such thing as a “pro eternal hell book buyers club.” Nothing remotely like it exists, even figuratively speaking. For one, lexicons like this are extremely expensive, and so very few non-scholars own them in the first place. Second, these are extremely lengthy works – thousands of pages with thousands of individual entries – for which an absolutely enormous amount of work has gone into producing them; and if you think that people are attracted to them just because of one little entry for one word that you don’t like, you’d be gravely mistaken.
And as always, if you have some criticism about the translation/interpretation of particular texts that appear in the controversial “pert. to a period of unending duration, without end” sub-entry for αἰώνιος in, say, BDAG, you’re free to elaborate on this. Again, here it is in full:
③ pert. to a period of unending duration, without end (Diod S 1, 1, 5; 5, 73, 1; 15, 66, 1 δόξα αἰ. everlasting fame; in Diod S 1, 93, 1 the Egyptian dead are said to have passed to their αἰ. οἴκησις; Arrian, Peripl. 1, 4 ἐς μνήμην αἰ.; Jos., Bell. 4, 461 αἰ. χάρις=a benefaction for all future time; OGI 383, 10 [I b.c.] εἰς χρόνον αἰ.; EOwen, οἶκος αἰ.: JTS 38, ’37, 248–50; EStommel, Domus Aeterna: RAC IV 109–28) of the next life σκηναὶ αἰ. Lk 16:9 (cp. En 39:5). οἰκία, contrasted w. the οἰκία ἐπίγειος, of the glorified body 2 Cor 5:1. διαθήκη (Gen 9:16; 17:7; Lev 24:8; 2 Km 23:5 al.; PsSol 10:4 al.) Hb 13:20. εὐαγγέλιον Rv 14:6; κράτος in a doxolog. formula (=εἰς τοὺς αἰῶνας) 1 Ti 6:16. παράκλησις 2 Th 2:16. λύτρωσις Hb 9:12. κληρονομία (Esth 4:17m) vs. 15; AcPl Ha 8, 21. αἰ. ἀπέχειν τινά (opp. πρὸς ὥραν) keep someone forever Phlm 15 (cp. Job 40:28). Very often of God’s judgment (Diod S 4, 63, 4 διὰ τὴν ἀσέβειαν ἐν ᾅδου διατελεῖν τιμωρίας αἰωνίου τυγχάνοντα; similarly 4, 69, 5; Jer 23:40; Da 12:2; Ps 76:6; 4 Macc 9:9; 13:15) κόλασις αἰ. (TestReub 5:5) Mt 25:46; 2 Cl 6:7; κρίμα αἰ. Hb 6:2 (cp. κρίσις αἰ. En 104:5). θάνατος B 20:1. ὄλεθρον (4 Macc 10:15) 2 Th 1:9. πῦρ (4 Macc 12:12; GrBar 4:16.—SibOr 8, 401 φῶς αἰ.) Mt 18:8; 25:41; Jd 7; Dg 10:7 (cp. 1QS 2:8). ἁμάρτημα Mk 3:29 (v.l. κρίσεως, κολάσεω, and ἁμαρτίας). On the other hand, of eternal life (Maximus Tyr. 6, 1d θεοῦ ζωὴ αἰ.; Diod S 8, 15, 3 life μετὰ τὸν θάνατον lasts εἰς ἅπαντα αἰῶνα; Da 12:2; 4 Macc 15:3;PsSol PsSol:3, 12; OdeSol 11:16c; JosAs 8:11 cod. A [p. 50, 2 Bat.]; Philo, Fuga 78; Jos., Bell. 1, 650; SibOr 2, 336) in the Reign of God: ζωὴ αἰ. (Orig., C. Cels. 2, 77, 3) Mt 19:16, 29; 25:46; Mk 10:17, 30; Lk 10:25; 18:18, 30; J 3:15f, 36; 4:14, 36; 5:24, 39; 6:27, 40, 47, 54, 68; 10:28; 12:25, 50; 17:2f; Ac 13:46, 48; Ro 2:7; 5:21; 6:22f; Gal 6:8; 1 Ti 1:16; 6:12; Tit 1:2; 3:7; 1J 1:2; 2:25; 3:15; 5:11, 13, 20; Jd 21; D 10:3; 2 Cl 5:5; 8:4, 6; IEph 18:1; Hv 2, 3, 2; 3, 8, 4 al. Also βασιλεία αἰ. 2 Pt 1:11 (ApcPt Rainer 9; cp. Da 4:3; 7:27; Philo, Somn. 2, 285; Mel., P. 68, 493; OGI 569, 24 ὑπὲρ τῆς αἰωνίου καὶ ἀφθάρτου βασιλείας ὑμῶν; Dssm. B 279f, BS 363). Of the glory in the next life δόξα αἰ. 2 Ti 2:10; 1 Pt 5:10 (cp. Wsd 10:14; Jos., Ant. 15, 376.—SibOr 8, 410 φῶς αἰῶνιον). αἰώνιον βάρος δόξης 2 Cor 4:17; σωτηρία αἰ. (Is 45:17; Ps.-Clem., Hom. 1, 19) Hb 5:9; short ending of Mk. Of unseen glory in contrast to the transitory world of the senses τὰ μὴ βλεπόμενα αἰώνια 2 Cor 4:18.—χαρά IPhld ins; δοξάζεσθαι αἰωνίῳ ἔργῳ be glorified by an everlasting deed IPol 8:1. DHill, Gk. Words and Hebr. Mngs. ’67, 186–201; JvanderWatt, NovT 31, ’89, 217–28 (J).—DELG s.v. αἰών. M-M. TW. Sv.