WOW... i think you're right in all of your conclusions and if you want an opinion, I'd go with option 1 for a week at least and then stop and decide either go for option 2 or 3. I would also tend to think that if option 1 fails for a week without any substancial improvement, then you're in the path for one nap a day and then, there will be no much left to figure out, just try for a later nap time and try that nap to be around noon and as long as possible.
While you try option 1, and in cases nap 2 does not happen or is too short, go for an early bedtime, even as early as 530 or 6PM to help Lucy catch up on lost sleep and to have time left for relaxing and long wind downs so she can settle easier at bedtime.
Teething molars, yes a very likely posibility (given lucy's age and restlesness at nights, the gassiness and the chewing hands )that can be helped with pain meds (as long as your pediatrician is ok with it, he will indicate you the doses and frequency). Molars can take even up to 2 months to pop up.
Another thing that could explain the restleness at nights can be overtiredness caused by the lost sleep and this can be solved with the earlier bedtime. If you're gonna deal short naps with wi/wo you might as well try it for night wakings.
Criticism? well that's something i would expect you never got from this site
. Your usual routine/schedule sounds like a dream to me also but i think that now that Lucy's into toddlerhood she might need a bit of tweaking, she's more mobile and probably ready to switch to one nap but to make sure, you need to work on a method at least for a week consistantly to figure out what she needs. Let us know about your progress and findings while this happen. Many useful ideas and words of sympathy will come up.
Good luck!