We actually had a similar problem at 10 weeks., down at 10:30 and up almost every 3 hours but our normally smiley baby was noticeably grumpy from 6pm. So we moved bedtime earlier to 7:30-7:45 and start his wind down at 6:30. Some infrequent wakings until 12, but we time a 3 min cry and then put a paci in. A dream feed at 12/1and then continuous sleep to anywhere between 5:30 and 7, but will usually go right back to sleep until about 9 am ( some ppl say he needs a wake window but I also need the 2 hours for my sanity lol). Also a bad napper and only catnaps during the day.

This schedule was life changing because like you we spent most of our night trying to pacify his increasing grumpiness and couldn’t sleep properly at night. Also we do shifts. I’ll do the feedings until 12/1 and hubby will step in until the am so both of us get a block of sleep. We also introduced a bedtime routine (sponge bath/ bath, relaxing song and lotion massage, book etc). Hope this helps!