What comes after the ducentiquinquagintasexions?
I'm afraid the words you mention were already formed incorrectly and inconsistently.
I see some were formed from distributive numbers + an unknown suffix -ion (like quaternion).
Others were formed from cardinal numbers + -nion (like trigintaduonions)
Others again were formed from a cardinal number + something that doesn't look like a Latin word + a suffix that looks like -onion (sexagintaquatronions).
The ones that would be several separate words in Latin are the most problematic. Consider the cardinal number triginta duo, "thirty-two". Normally in Latin, if you wanted to turn that into a distributive number, you'd change both words into their distributive forms: trigeni bini "thirty-two each". Then if you want to add -ion to the stem of the last word and turn them into a single word, you will get trigeni-bin-ion.
The way some of the words in the list were formed, on the other hand, is by changing only the last word into a distributive number and keeping the other one(s) cardinal: triginta-bin-ion.
The Romans would normally write larger numbers as separate words. But, if we ignore that, using something based on all distributive numbers would seem closer to the Roman way, like trigeni-bin-ion above. I will provide both options; first I give [all distributive + -ion], then [cardinal(s) + distributive + -ion]:
Quaternions (4-ions)
Octonions (8-ions)
Sedenions (16-ions)
Tricenibinions / trigintabinions (32-ions)
Sexageniquaternions / sexagintaquaternions (64-ions)
Centeniduodetricenions / centumduodetricenions (128-ions)
Duceniquinquagenisenions / ducentiquinquagintasenions (256-ions)Quingeniduodenions / quingentiduodenions (512-ions)
Miliaviceniquaternions / millevigintiquaternions (1024-ions)
Binamiliaduodequinquagenions / duomiliaduodequinquagenions (2048-ions)
Quaternamilianonagenisenions / quattuormilianonagintasenions (4096-ions)
Note that distributive forms of thousand in Latin are a bit different from lower numbers, and I couldn't find any examples of their use combined with lower numbers: I only found passages with "three thousand each" in the HP Latin corpus, not e.g. "three thousand two hundred each". Note also that in Latin some words have two (or more) alternative forms, like triceni/trigeni "thirty each"; I have used the commonest alternative in each case.
Following the Latin prefix tables from phrontistery's reference, they would probably be:
512-ion: Quincentumduodecion
1024-ion: Millevigequaternion
2048-ion: Duomillequadragoction
4096-ion: Quadrimillenonagesextion