There is another problem that comes with having water in the wheel. Unbalanced wheels. The water in the wheel will all drain down to the bottom, creating a heavy spot in the wheel. When the wheel starts moving, it will shake the entire vehicle.

Squeeze as much water out as you can. In my experience, it doesn't dry out very easily. I haven't tried putting them out in the sun though.

I've poked holes in the surface of my tires with a hobby knife and spun them with the air compressor. That gets a lot out. They balloon up pretty good with the compressor blowing across them.