I've only recently started to have good luck (dry sheets) while sleeping on my side, and thought I'd share my ideas and maybe get some new ones.
I'm just big enough to call a medium bambino too small, and have been using M4's since they are in between bambino medium and large. But for overnight, I've been using a bambino large with a totaldry booster. I'm placing the booster in the front so it ends where the padding in the diaper ends, so the other end of the booster is about in the middle of the crotch.
For taping, I've been trying for a snug fit with the top tapes, just about where the padding in the diaper ends. For me, the blue pulls on the tapes are right about where the factory folds are. Then for the lowers, I've been taping in between "down" and "in", as a compromise, in as far as I can go at the bottom of the tape land. This causes the diaper to bulge out in the front and create a pocket in the front of the diaper where there's open space, but yet fits snugly around the legs AND around the tummy. This seems to really do a good job of not leaking.
Pointing down is not really negotiable, it's required. But I've found that by morning I have saturated the booster from back to front, and often not even touched the diaper padding in the crotch. The big issue seems to be gravity pulling pee down the front wing of the diaper, and that seems to be the key for leaking or not leaking.
SO... I was noticing that just about every brand of diaper is narrow in the front wings. Most diapers have wider wing coverage in the back, but for side sleeping guys, that's needed in the FRONT. I tried putting on a bambino backwards but it didn't fit well, I may try it again though. I've also tried placing a totaldry booster sideways across the front top of the diaper, wing to wing, and that seemed to help also, but seemed to need padding just below that where the crotch is transitioning to the wing. It seems that for side sleeping, the crotch and the back of the diaper are of no value, it's all in the front, specifically in the wings.