J.R.
Try a larger size diaper (regular or overnight) size 5 maybe.
Or, try taking out the cotton stuff inside a sanitary napkin to use as an insert- tried that with my son but it didn't work too well.
Or, try dressing him in a snug-fitting onesie over his diaper so that it holds the diaper close to him. Is he filling the dipaer or just missing? Sometimes with my son it seemed more like he was missing rather than soaking the whole thing through so getting a snug fit helped.
And to save time in the middle of the night when/if you have to change crib sheets, double-sheet the crib (so from the mattress up it's mattress, waterproof cover, sheet, waterproof cover, sheet). Just peel off the wet layers and put dry baby back down rather than make the crib again.