Why won’t my 3 month old sleep at the end of his wake windows?

Writing this with tears in my eyes as my 3 month old screams in my face. I have no idea what I’m doing wrong and why I’ve never been able to sooth my own baby. He’s always been a horrendous sleeper, even as a newborn. I can tell he’s tired, he’s probably chronically overtired at this point, but nothing I do will get him to go to sleep peacefully and calmly. Things always just escalate until he has a complete meltdown and falls asleep from exhaustion. Things I’ve tried to date: rocking, bouncing, shushing, nursing to sleep, black out blinds, red light, white noise, carrier, stroller, etc. Pretty much all the standard advice. Currently we bedshare (not really by choice, but out of sheer desperation for a bit of sleep at night). He’s exclusively breastfed. I try to keep wake windows of between 1.15 hours to 2 hours, but he won’t fall asleep until way after the window has ended and he has truly exhausted himself and has a meltdown. I’ve tried trying to put him down earlier (before sleepy cues even start) and I’ve tried later (after meltdown has started), but still the same thing happens. I’ve tried an earlier bedtime and a later bedtime. I’ve tried giving him more stimulating activities during wake windows and also keeping things low stimulation. I’ve taken him to a doctor and had him checked and he is otherwise in perfect health. I didn’t want to sleep train as I wanted to just follow his lead, but as we get closer to 4 months I’m getting so desperate. I’m exhausted and miserable. He’s exhausted and miserable. We never leave the house anymore or see anyone because all day is just a sleep battle. What do I do? Tell me it gets better 😭