Look into rubber-soled boots made for wading - as in with stocking-foot waders.

Cabelas, LL Bean, and other companies make something suitable.

I've been using a pair of the old-style Patagonia 'marlwalkers' - which are deisgned for wet-footing on coral - for a number of years. The new style is lower and with a less-luggy sole.  I use my for wading streams all summer long, and they go on canoe trips too.

Wading boots are generally pretty tough and protective - and they don't rot out from under you.