So most people don't actually summit Rainier?
I've never climbed it, myself, but that's my understanding... it's another 45 minutes walk around the rim from the dog routes to gain like 8-10' to the actual highest spot, so most people just opt to call it quits at the rim.
I dunno, I still tagged it last time even though it was a few minutes out of the way. There's a huge trough from the DC side to the side with the summit "bump" so, quite a few head there.
As for pissing on the summit, generally, those that plan ahead piss a few minutes before getting there. Back to the OP - why not piss before the bergschrund on Hood? (or in it) :-)