Too early to sleep train?

So my baby girl is 3 months old, which I think is probably a little young to sleep train. However, she is a terrible sleeper. She always has been. We got zero sleep in the hospital and the first couple of weeks. She did start to sleep better at night after that but about a month ago she started waking every hour or two again. Still a terrible napper as well. She only naps on me because it takes upwards of 2 hours to get her to lie in her bassinet for a nap. I just dont want to sacrifice her sleep for that.

To get her to sleep independently at night, we have a sound machine, fan, diffuser, blackout curtains, even that Magic Merlin sleepsuit. The environment is there. We also have a decent sleep routine where we read, cuddle, pray, and make sure we dont talk after it's bedtime.

We don't let her cry in her bassinet at all. I usually try to nurse her to sleep but lately that's not working very well because she wakes when put down. So then we bounce her, nurse her again, repeat until she finally stays asleep. Last night it was after 9 when she finally gave in (we started at 7:30). Even then, she never slept longer than 2 hours. I am exhausted.

In regards to general health, she is EBF and eats well and often during the day. In between, she is happy and smiles a TON. She laughs, coos, and usually doesn't cry unless she can't see me or is hungry or tired. She is a wonderful baby! Just hates sleeping. I want her to be healthy and rested so I thought we'd try some sleep training (I don't want CIO) but have read you shouldn't try until 4 months.

Does anyone have any tips or suggestions? I feel like we've tried everything! Thanks in advance.