Otherwise, you clearly need some serious trail-runners, which by design are shoes with stiffer midsoles than road shoes, more grip in the outer soles, and more supportive (and waterproof) uppers. Fortunately, there are lots of fine shoes from which to choose. One that should top your list is Montrail's Hurricane Ridge ($125; www.montrail.com). It's a sturdy, well-made trail-runner with an aggressive sole and a Gore-Tex XCR liner to help keep your feet dry. And its dual-density EVA midsole helps stabilize your foot while providing good cushioning.
Take a look as well at Salomon's XA Pro 3D (also $125; www.salomonoutdoor.com). Like the Montrail shoe, it has an XCR liner and a grippy outsole. But its triple-density midsole and nylon footplate offer more sophisticated motion control and cushioning than the Hurricane Ridge. You'll want to try on both and get a sense of what feels the best.
I realize that both these shoes are at the high end, price-wise, especially if you buy two pairs. But, you could buy a second pair of shoes with less intense weatherproofing at a lower price point to save yourself some dough. Those then become your "dry day" shoes, the more weatherproof shoes the wet-run models. Nike's Air Zoom Orizaba ($90; www.nike.com) or the Asics Gel Eagle IV (also $90; www.asics.com) will save you a few bucks, while still yielding excellent trail performance with a bit less moisture protection. Alternatively, you can buy two pairs of the cheaper shoes, then keep your feet dry with a pair of Rocky Gore-Tex socks ($50; www.rockyboots.ca).
Check out the crud-busting lineup of kicks in Outside Online's Trail-Runners Buying Guide.