Actually, the mixture does change when the engine is loaded "enough". If you're running up the hills at wide-open throttle (WOT), usually the feedback mechanism in the Engine Management System will be disabled and the mixture will be fairly rich. Ditto if you keep pumping the gas pedal; most EMSes will richen the mixture when the throttle goes from less-open to more-open to help acceleration.
But if you're cruising up the hill at a steady part-throttle, the mixture should be fairly near stoichiometric.
The rotten-egg smell is sulfur. Among other things you can try, another brand of gasoline might help. I recall that Chevron and Shell were rumored to be relatively high in sulfur content, but that
was just a rumor that I have not been able to verify.
I agree with Wayne, though--find a way to check your mixture and see what that has to tell you. Catalytic converters can indeed fail without blocking the exhaust (to the extent that you will notice just driving around on the street) so the "does it make less power?" test is not definitive.
Of course, you could always wait until you have to pass some emissions test....
--DD