I love a good bear thread!
First on a serious note, and to answer your question. Like most folks here, I personally would not feel real comfortable with anything less than .44 mag. If you are most comfortable with your H&K USPc in .40 cal. I would buy some solid bullet ammo for it.
I didn't look, but Cor-Bon or Buffalo Bore may make a 180gr. solid like a JSP, or a JFP. They do not suggest that you use all lead bullets in a polygonal barrel, but I have the exact same gun that you have, and I have shot total lead bullets out of it with no problems.
The important thing is that you buy enough of these solids so that you can test fire a bunch and make sure they work reliably in your USP. I don't think you will have a problem though, because mine has eaten everything I have ever put through it without a hitch.
If you won't take a magnum, this will have to do.
On a funny note, on one of the many bear threads that have been posted, a guy asked how he could tell the black bear from a brown bear (other than the color, because some black bears can be brownish in color.)
The guy that answered him gave one of the best answers I have ever heard. He said, " If a bear is chasing you, quickly climb a tree. If the bear climbs the tree and eats you, it was a black bear. If the bear knocks down the tree and eats you, it was a brown bear."
Good luck on your trip.