Dont be too quick to blame the bike.
I've ridden thousands of miles with top case and side cases, empty, fully loaded, not installed, installed, two up and solo at gps indicated speeds of over 100 in all weather, warm, cold, windy, snowy, rainy, well you get the idea, and haven't had any stability problems with the strom.
check your tires for correct pressure, chain/rear wheel for alignment, even the front wheel for alignment. Play with the suspension settings, thats what they are there for. Ride properly, don't overgrip the bars.
As for the seat, well, I disliked my stock seat initially, but have gotten used to it, especially after installing bar risers. I just rode my friend's '02 strom with corbin seat and didn't like that one at all. After 10000 miles on my seat, I really dont have a problem with it, now.
YMMV
chris in boston