I have some Nalini with relatively thin pads, but you're going to have to just look around. I've got a couple of brand new pair of Performance Ultra shorts, and the pad is really massive. They work OK for spinning class, but I wouldn't buy bibs for road wear now that I've seen what the pads and other materials are like.

Also, if padding is getting bunched up, it's more likely that the shorts are just too big on you.