I was shocked when I saw the word "latest" in a Latin book. The book's English translation implies it is related to "latus." The next word "alteque" would have suggested an adverb "late" + "-st," but I don't know of any "-st" suffix in Latin. Had it not been for the other occurrences of "-st," I would have dismissed it as a scribal error. I assume this "-st" is a contracted version of "est." Contractions might not be formal, but they are probably still classical.
I was going to hypothesize a set of three paradigms based on "possum," which is the archetypal word with "esse" inside where the prefix isn't from a preposition. The hypothesized contracted perfect passive would do to the -sus/-tus-stem what the perfect active does to the *-uus/*-vus/*-wos-stem. This should not be confused with the poetic syncopated perfect active, which deletes the u/v, and such syncopation would be impossible for the hypothesized pluperfect and future perfect lest they confusingly overlap with the active. A concern is that there aren't many examples attesting this.
Alternatively, did the contracted form inflect for gender? There are 4 occurrences of "captust". There are also "multumst" and "iactast" as mentioned by Reddit.
"Neccessest" occurs many times. However, it could be caused only by the indeclinable "necesse," because "ipsest" is also found. "necessum" unfortunately overlaps with the alternative declinable past participle. Google returns some but potentially low-quality results for "necesserit" and "necesserat."
What would you put for the contracted perfect passive's conjugation table?