There are many factor than just setting the angle of the saddle, your saddle should support you well, without it feeling like you’re sliding forward onto the handlebar putting a lots of your body weight on it.
It sound like you got the angle right, the next part is the fore and aft position that’ll help with your back, but from what it sound, I guess setting it a little bit further back should help.
If it make it worse, try setting it slightly forward (but not too much that, like the angle of the saddle, put too much of your body weight onto the handlebar).
Once you got the saddle to bottom bracket distance and angle sorted, then you can concentrate on what stem length to go for.
It’s quite difficult to explain generally, Steve Hogg is the man to go to when it come to bicycle fitting, so his article, hopefully should make slightly more sense;
Seat Setback: For Road Bikes
Hope this help.