Hello, Im not an expert but can offer a bit of advice from experience... my LO is turning 14weeks this week(3months & one week). He also started eating every 3.5-4 hours a couple of weeks ago which ive now accepted as his natural transision and give him food every 3.5-4 hours depending on when he wakes up from his naps etc. Its working great as he is eating full bottles. The naps vary every day and one day he sleeps as he did on 3 hours EASY while the next he takes two 2hours naps and the cat nap... so i just see it day by day and hopefully it will all continue to happen naturally and by 4months we ll be on a solid 4hours routine.
As far as food he now only wakes once a night for food during the 12 hours of sleep.
How much does he eat at 1.50am? As this should be the firs feed to be "removed"?
For us it happend naturally once i took the amount of what he used to eat at 2am(in our case) and gave him that amount during the day, i increased every feed a little bit (not given him an extra feed).
And that he is holding food for longer time than before he sleeps longer streches during the night going 8hours sometimes but mostly 6 hours straight:-)
I recommend for you to try giving him more during the day so you can get longer streches during the night, im sure you need it:-)
Good luck!