It's very common for LOs who are teething to manage well during the awake time in the day, but find napping difficult. It is also common for teething to show itself more at night which you are not experiencing, but as you've said he is getting only 15-30 mins nap he is likely so tired by BT he is just crashing out. I think it's worth trying some meds 1 or 2 days to just see if it has any effect. If not then I wouldn't continue. I found it very difficult to look into my baby's mouth to see or feel for teeth coming so went solely on mood/crying.
Have you tried APOP (accidental parenting on purpose) with him for naps - ie that you hold, cuddle, put in the stroller, or car, rock...anything at all to get him to sleep and stay asleep? Sometimes when a baby isn't napping well they need lots of encouragement and soothing to help them to nap and nap a decent length of time, this teaches them to nap well as the rest period becomes habit. Of course you don't want to be 'stuck' with AP methods but they can help to form the napping habit for LO and from there you can begin to encourage self settling again.
You said the Binky is now gone, do they have alternate lovies for comfort?
Also, what method did you use to teach your twins to self settle?
