Hiya, I suspect you're in 2-1 territory although that doesn't necessarily mean he's ready for one nap. Just out of interest, what did his day look like when he was getting longer naps at home? How are the nights? What do you do when he wakes in the morning? Get him up straight away or let him chat/fuss/doze,in his cot until a fixed time that you've decided on? Please take my suggestion with a pinch of salt, but looking at his current tendencies, you say that putting him down earlier in the morning results in the same length nap (30mins), so have you tried putting him down earlier and capping that nap shorter, say, to 20mins? Then you might find he's tired enough for a good length nap in the afternoon and be less tired for BT. This would only really work if he's able to go down quite UT in the morning - some LOs can, others can't. I personally like to stick to a fixed 'get up' time, regardless of actual wake up time, and then fix the time of the first nap. That seemed to prevent the WU time from getting too ridiculously early. Also he just seemed to cope better with shorter A times in the morning but a really short first nap meant that he was nicely tired for the pm nap. But tbh this all worked much better with DS than it has/is with DD
So, bearing in mind that this is just one option and that others may chime in with alternatives, this is what DS did at around 13mo:
Wake up any time from 5.30-6.30am
Get up 6.30am
Nap 1: 9.30-9.50am
Nap 2: 1-3pm
BT: 7pm (had to push this later as he approached 1 nap, it ended up at 8pm!)