Waterproof shoes will rarely be waterproof 3 hours into a cycle, it's just a long time for a piece of clothing with a large hole in the top to keep water out. The rest of your clothing must also be waterproof as if the pants are not waterproof, water gets in the top. Also need a good jacket. For heavy rain you need a full setup.

For commuting I have a pair of Columbia outdry hiking shoes. If it's raining heavy I have a pair of waterproof "breathable" trousers and over them a pair of regular hiking gaiters. This does a great job at keeping heavy rain out for at least an hour.

It's not a typical cycling setup, but it works for hiking so I assumed it would work for cycling and it does. It is used by more than I, an accomplished athlete who cycles a lot recommended it to me.

Have realistic expectations, nothing is waterproof in definately and the longer you're out in a downpour the more time water has to find all the little paths in.