It must be very challenging trying to make the "best" position.

FWIW I would like to allay one of your fears. Because you had a long second stage with your daughter that does not mean you will with subsequent children. To birth a posterior baby on your back is very far from optimal and I would offer it likely protracted your second stage.

I too had a posterior baby and I too was on my back (due to epidural headache) & I too had a very long second stage.

My other live babies were 20mins for DS, 2 pushes for DD2 and one big one for DD3.

They were all very active births, using water (I would very very highly recommend this it is known to be very helpful for SPD sufferers) & lots of movement.

I don't think you will find any studies as such to help you decide as I would assume that it's clearly physiologically easier to recover from a vaginal birth with SPD than with pelvic surgery that c/section requires. (so therefore studies are a bit moot yk?)

I think you're just going to have to really go into yourself on this one. Examine your feelings, listen to your wise woman voice... Take lots of time - you have plenty up your sleeve... Good luck!