The way I put them in, there's no pressure pushing on them through the night since they're so far in. And I'm a side sleeper, too.
What almost works for me is using two differently sized earplugs and putting the smaller one in the pillow-side ear, because the pillow pushing on the ear canal causes it to seal despite the smaller plug. But when I roll onto my other side several times a night, I'd have to wake up and swap ear plugs. It's not feasible. :(