Cycling_guy, I am a side sleeper and share your frustration at leaks.
Basic strategies:
1 - Choose the right diaper. You may need faster absorption. A diaper with more fluff is good. Try a Dry 24/7.
2 - Add a booster pad to the diaper for more absorption.
3 - Tape the diaper more snugly and reinforce the tapes so they will not pop off
More complex strategies:
4 - Wear two pair of plastic pants - the first sized for disposables and a larger pair on top. The elastics of the large pair should make contact with the thighs below the elastics from the first pair. This should keep a couple of ounces from leaking out.
5 - Double diaper with slits cut in the shell of the inner diaper. I use a Dry 24/7 over a Seni. Works great but increases the cost.
6 - Wear a day-weight cloth diaper over the disposable. Works great and you only need to wash the cloth diaper if there is a leak from the disposable.
Best strategy:
7 - Wear cloth diapers
I have done all of these but now wear cloth exclusively at night, except when on travel.
--John