Hi there
It's great your Lo has started to self sooth for some of his sleeps
Great!
I'm afraid that going to bed at 2am and not waking for the day until around 11am is something that just needs to be changed - by you. He is not likely to just change this on his own showing you cues or with small tweaks in his nap routine. If you want this to change then you need to implement a clear routine and stick with it - he will cry yes, chances are though it will be just 3 or 4 days of absolute consistency with the day/night shift to begin to see changes.
There are two options really
1. go directly to an acceptable routine and ride it out. Wake him at 7am keep him up until nap time, cap nap at 2hrs, keep him up a full A time and continue to evening with 7pm BT.
or
2. slightly slower (but you still need to keep moving on it and it is still up to you not him to instigate change).
day 1 WU 9am, full A time, nap capped at 2hr, continue to BT 9pm
day 2 same as day 1, WU 9am, proper day routine, BT 9pm
day 3 WU 8am, full A times and naps capped at 2hrs max, BT 8pm
day 4 same as day 3, 8am - 8pm
day 5 WU 7am, full A times and naps capped at 2hrs max, BT 7pm
day 6 and thereafter same as day 5, 7am - 7pm
In either case (going quicker or slower) the following applies:
- in "day" (that is all time from WU to nap time, between all naps, up to "night" which is BT) you need lots of natural light, normal household noise and activity
- in "night" (that is from the required BT all the way to the required WU time) you need a dark room, dim lights when doing night feeds, no noise other than shushing or white noise, no conversation other than the minimum (ie "let me pick you up for a feed", "I'm going to change your nappy now" or "night night go to sleep"), no singing or chit chat about things, no other distractions.
- during A time you need to keep him awake, if he starts to nod off you need to do whatever you can to distract him and wake him and keep him awake until nap time
- at nap time you need to keep him in a dark quiet room and repeat that it is time for sleep, set the environment and cues for sleep, if he doesn't sleep you keep him in there soothing him with shush/pat (or a firm hand doing a little rocking in the cot if needed) either for an additional 45 mins or until the end of nap time (if he sleeps a short nap of 20 mins I suggest only staying 45 mins trying to resettle, then feed a little earlier than the routine)
Some LOs just seem to run on a day length that is not 24hrs - if you allow them to shift to their own day length the result is day/night switch and antisocial sleeping times. My own DS seemed to run on a 23hr day and was forever trying to get to bed for night sleep an hour earlier, I had to stretch him to BT as he woke early anyway - left to his own devices I believe he would have continued to go to bed earlier each night and wake earlier each morning - not pleasant.
You will need to be very consistent on this to make changes, and it may help to write out on paper your plan for each day (the full routine) so you have something to follow when you are feeling very tired.
Hope this helps