In classical times, foreign names (except Greek ones) were adopted into Latin based on their sound, not spelling. Suppose Caesar conquered a tribe in Gallia living on an island they called something like Betuwe (I don't know the exact sound/spelling); this word would be related to him in speech by messenger or a local inhabitant. He would hear it well or not so well, and make up an image of what it sounded like in his mind. Then, when writing, he would find letters that might best approximate the sound he had in mind. So an inhabitant became a Batavus. There is nothing in Latin that rules out bet-, but it was still changed. The same applies to the -u-. The ending -we was decidedly un-Latin, though.
In summary: I don't think you could expect much consistency in classical Latin, it was all done ad hoc. Only in contact with cultures having well known writing-systems, like Greek and possibly a few in the Near East, would they usually apply a consistent transformation. But it can be seen that Greek names adopted by prae-classical Latin were transformed using different rules (or few at all), despite close contact between Greek and Latin in the archaic age.
In Early Modern times, the culture of writing had been established much more amongst the vulgar languages in Europe, so I would expect a bit less chaos and deformation. Even so, the names of simple migrants were probably often still transformed ad hoc, based on the sound. A farmer from the region of Kiev migrating to Italy might not know how to spell his name, or, if he did, not how to translitterate it into Latin letters. And the Italian scribe taking his name might not be happy with the translitteration anyway, and turn it into something that was pronounceable.
That said, for a most historically plausible Latinisation, it might be best to look at those historical names you found:
Cavalot, Covello, Covalea, Coveller, Covelley, Coveley
The consonant cluster -lch is un-Latin. Even -ch is un-Latin except when archaic. A noun ending in -uc would normally be un-Latin as well, as is the letter k except in archaic words. Only Covello and Covalea might conceivably sound Latin because of the endings: -ot (French?) and -ey (French/English?) are not possible. But the stems themselves of all forms would be possible (caval/coval/covell/covel). Now, in the late Early Modern period, it was common practice to Latinise surnames using the ending -us, at least around the North and Baltic Seas. As you said, the Slavic suffix -chuck is probably best removed. I believe common suffixes in Early Modern Latinisation were -n-, -in-, -ini-, and -i-, also because I think those often denote parentage or local origin. You could compare the particles de and van with Chauvin and Herman to those suffixes qua meaning, and thus also to -chuk. But, again, even in that period, there was probably still a lot of chaos and Latinisation ad hoc.
So what combination of stem + suffix + ending to choose? I would probably Latinise Kovalchuk as (caval/coval/covell/covel) + (i/in/ini) + us, and I think one choice would be as good as the others. So Covalius would sound as authentically 17th-century as would Covellinus. If you want to go classical style, you can basically pick anything that sounds nice in Latin (including these forms here).
P.S. I suspect you hadn't received an answer yet only because your text, while all relevant, is very long.
P.P.S. In Morris → Mauritius, this was done because, in many cases, the real origin of the name Morris is actually Latin Mauritius (related to the Moors, Mauretania). So, if you can find a Proto-Indo-European root for Slavic Koval, and if you can find a Latin or possibly other European reflex (word derived from the root), you might use that for a stem. It would be a very elegant solution, though the ones based on actual historical usage like Covalius could still compete with it, simply because of their historicity. If you have an etymological dictionary of Slavic, you could probably find this Proto-Indo-European root.