What is the natural way in which to derive verbs from nouns, where their meaning is to furnish something with the thing named by the noun? For example, what might one call an omega furnished with an iota subscriptum, if we wished to add only a participle; an omega iotatum? Or would this rather mean an omega turned into an iota?
If we are looking for a verb, I think your suggestion of iotare is actually a very good one. You observe that iotare might mean several other things(*) like making a iota or becoming a iota(in the passive (**)), which is apparently correct indeed, but that's how verbs work; they might mean different things and IMO we should not be deterred by this.
We can take the highely relevant example of the verb corono which is derived from the noun corona per Wiktionry, it might mean several things, but among them the required meaning:
to furnish with a garland or crown, to crown, wreathe (L&S dictionary)
(*) We might consider two examples: corporo (from corpus) and radio (from radius), it seems that corporatus is more of the meaning of "turned into a body"(as the active is rather to "form a body"), but with the case of radiatus the meaning is rather "shining" or "furnished with radia" (e.g. corona radiata white matter in the brain). But even corporo means according to L&S "to furnish with a body" which, as previously the body was not existing, is almost identical to fashion into body
(**) For the active meaning to become a iota, it can be argued that a better suggestion would be iotabesco, i.e using the suffix -sco, like rubesco.
But if we only need "participle" or adj. I second @Asteroides, just to add another example manubriatus (furnished with a handle (manubrium)), where, again, it seems there is no verb; one may claim, as suggested in your comment, that those example are participles of defective verbs, but I find no problem with that as long as the meaning is clear.
There is a suffix -atus that forms adjectives with this kind of meaning. Like English -ed, it looks the same as a common past participle ending, but the words are not actually past participles: no corresponding finite verb is necessarily in use.
For example, dentatus means “toothed” in the sense of “having teeth”; it is not a participle meaning “having been toothed”, and no Latin verb dento, dentare exists to my knowledge.