Paucis verbis rem divinam facito
... [many dictionary entries]
The Godly will accomplish much with few words ? ? ?
Let's take it in stages.
(1) The verb is "facito". Your dictionary entries show that it is either the second or third person future imperative of "facio": a common word with many different shades of meaning (OLD lists 30 different meanings), but basically "do" is usually a good starting point, though one often has to move to a more specific English verb once one knows what sort of "doing" is involved. So we have something along the lines of "you (singular) shall do" ("thou shalt ...") or "let him do". (One might quibble with the "future", but for present purposes it will do.)
(2) There are two nouns here: "verbis" and "rem". Check the endings. "Verbis" is either a dative or an ablative plural of the 3rd declension neuter verbum (word). Rem is the accusative singular of the 5th declension "res" (a paradigm example of this rare declension, and a very common word: "thing").
(3) We then have two other words to account for: "paucis" which must be a dative or ablative plural of paucus -a -um (a little a few) either in the masculine or the neuter. We only have one (neuter) noun it could go with, namely "verbis". So we have "a few words" in either the dative or the ablative. I would guess ablative "with/in (a) few words" -- a common expression. You got this right.
(4) This leaves divinam. It is evidently a feminine adjective (divina), which fits with res (a feminine noun), and is in the same case (the accusative). So we have a or the "divine thing". This is accusative and therefore probably the object of the verb: this is what is to be done.
(5) So if we put it together we have "you shall do a (or the) divine thing with (a) few words", which is puzzling.
(6) In fact, "res divina" (the nominative form of what we have in the accusative) is a stock phrase meaning "ritual" (you might need a big dictionary to ascertain that).
(7) So we can try again. Perhaps "Perform the ritual with few words". The "to" form of the imperative (sometimes described as future) is solemn and legalistic. So perhaps we would translate "Thou shalt perform the ritual with few words" This is as far as I could get without context, and the context might lead me to reconsider the translation. It's hard to know if you are right about something as odd and short as this without some context.
I'm not surprised you are having trouble, because these short sentences pulled out of context are pretty hard, and the subject-matter is not exactly mainstream, and I admire you for trying. But I think there may be a problem with your basic approach. You are going wrong because although you are pulling out all the possible meanings, you are not piecing them together, and you are guessing at the meaning based on the meaning of the words without working the grammar through -- though the very helpful dictionary entries you are turning up should help you with it. In your translation:
(1) You have treated "divinam" (singular feminine accusative adjective) as a plural nominative noun (which would, unless one meant "godly women" also be masculine). (Adjectives as substantives are not uncommon, but "godly" would probably
be "pius": divinus means divine of godlike
, which is not at all what godly means.)
(2) You have treated an imperative as a simple future -- and for that matter made it plural.
(3) You have inserted the word "much" which is not in the sentence, nor in any of the dictionary entries.
I've tried to set out above the general pattern I would follow in putting something like this together. The basic steps are: find the verb; group nouns and adjectives and work out their case; and then try to put it together, starting with an over-literal translation and working towards something that seems to make sense. I hope I don't sound too harsh; I don't mean to. You're starting off the right way by checking things up in the dictionary and so forth, but you need to concentrate more on the grammar and less on the root meaning of words, or you will tend to produce a jumble of similar ideas in quite a different order.