Man, I never fight Stamper in non-balloon mode. He's just too crazy.
My strategy has always been to attack Stamper right out of the gate - more often than not you can get a very good juggle on him. Then allow him too balloon up. Jeff is very easy to avoid while you whack at the defenseless Stamper. His fart bubbles are also very easy to avoid.
I usually try and juggle Stamper when he falls out of balloon mode. It's a 50/50 chance at this I find. If he gets good counters going I'll just run away and avoid them until another ballooning.
Once Stamper is toast Jeff is easy pickings. Knock him down, then run away (if you're low on health). You can even feed him a few bombs if your score is relatively high and you've got close to max bombs.
I don't think I've ever taken Jeff out first, unless it's one of those incredibly rare instances where I manage to get them both in a big juggle.
Once you perfect this method, you can knock Jeff down every now and then while Stamper is ballooned, so the solo fight against Jeff is a little shorter.