I have run a quick analysis using data from latinlexicon.org. I included adverbs ending in -ter (about 820). Most end in -iter (the rule). A good number end in -nter (which as you know are formed with syncopation regularly when the base adjective/participle ends in -nt). The remainders are a mix of declinables and indeclinables (e.g., propter is indeclinable so I excluded it). There were only a very few left, which can be summarized into three observations:
- Based on an adjectives ending in -t (which does happen to include the -nt participles): there is a syncopation that seems to suggest the rule is -titer = -ter.
- Based on an adjectives ending in -c (the only example seems to be audacter): there is a syncopation that seems to suggest the rule is -citer = cter.
- Based on an adjectives ending in -lis (facil, dificil, simil)
The next question becomes, are there a large number of adjectives in these categories that don't conform to the preceding observations? This is a difficult question to answer because there are so few adverbs that were recorded in Latin literature.
However, here are my anecdotal notes on the three categories of adjectives:
- This group is almost totally devoid of adverbs that haven't already been mentioned, but based on the production of -nter adverbs I would guess that it would hold true to a native Latin speaker. Honestly, most of the adjectives are place names anyway that rarely form adverbs. However, when they do form adjectives, the often use -e instead of -iter (most likely an old locative).
- Audacter seems to be the one exception to this rule. Most other adverbs seems to comfortably end in -citer not -cter (e.g., pugnaciter).
- These seem to comfortably form -iter adverbs (visibiliter, gentiliter). It seems like the only ones that form -ter adverbs are some of the "irregular" adjectives facil, difficil, simul, etc. (the ones that form their superlatives with -limus).
So, to answer your question with a mix of analysis and opinion, I would say only in one case would you want to syncopate, that being adjectives of the 3rd declension ending in -t (which definitely includes -nt) but not -c and not -l.
It is, of course, poetry. So I'm quite sure you could add and subtract an 'i' here and there and only the most picky editors would care. After all, Adele sings the word "hello" with 8 syllables.