Sorry to hear you are so run down by this. Nap transition phases can be very frustrating and very tiring.
A couple of options I can think of:
1. To increase A times gradually, but firmly, write down what your A time goal is and stick with it, ignoring sleepy cues, and continue the capped CN until A times reach close enough to 3hrs to be able to drop the CN
OR
2. Go directly now to a 2 nap day with set nap times. This is often hard for a few days, LO can become OT in the shorter term, but the bonus is that usually LO also gets into the new routine much faster so instead of A time increases dragging out for weeks you both have a bit of a rougher time but for a shorter time frame. This second option is often helpful for people who are at the end of their tether which is why I mention it. I might otherwise have suggested plodding on for another 2 weeks to get closer to 6 months but this route has worked very well with LOs of 5.5 months too. The other benefit for you is that there is not guessing of sleep times it's just set. Tracy used this method for putting LOs onto a routine - it can seem quite dramatic but it gets results.
Based on the times you have given for WU the day would look like this:
WU 6.30
A 3hr
S 9.30 - 11.00 (you can let him sleep up to 11.30 if he wants to)
A 3hr
S 2.00 - 3.30 (or 2.30 to 4.00 if first nap was 2hrs) (this nap might be 2.00 - 4.00 for a 2hr nap)
A 3hrs
BT 6.30pm if both naps were 1.5hrs. 7pm if one nap was 2hrs
LOs seem to have a natural nap length of either 1.5hrs (2 sleep cycles of 45 mins) or 2hrs (3 cycles of 40 min) so the routine depends a little on that although actually you can fully set this routine if you find that easier.
If he is LSN, does that change anything?
LSN can mean shorter nights and can mean ability to do very long A times (so don't worry so much about increasing). Generally if a LO can't do 12hr night but more like 10.5 or 11hrs we look at the day routine to allow for that and just don't expect 12hrs.
LOs can sometimes appear LSN and end up pretty average or even high sleep than others...just to confuse things. As example mine did huge A times in the morning but very short at the end of the day, always 10.5/11hr night never longer, so appeared LSN. However he held on to his nap for longer than many LSN toddlers and at 4yo, 5yo and now at 6yo is sleeping longer nights than most of his age peers.
I'll let you have a think about those options.