If you can feel the rivets you are definitely too far back in the saddle riding on the frame, rather than on the suspended section in the middle. Rivets or no you're going to get an uncomfortable ride.

That said, it used to be fashionable to file down the large copper rivets on the Brooks Pro saddle. Nothing stops you from filing yours down a bit, but be aware that those that aren't visibly copper are plated steel and filing will expose them to rust. It's OK if you keep them waxed or painted with clear nail polish, but you'll need to be attentive to that extra chore.