I don't really like the baggy shorts for the reason you said(feels like a diaper).
I usually just suck it up and wear the lycra shorts. You might want to try looking at these briefs they have at performance. They look like compression shorts but have a pad in the crotch area.
http://www.performancebike.com/shop/...egory_ID=1123#
Kinda steep at $18...