I gave up cycling shoes when they got wet and stayed wet. Switched to bicycling sandals with clipless cleats. Only footwear.
That is a point that many people miss. My solution isn't sandals though. Unlike most other bike shoes I have owned, I find that my sidis soak up almost no water. They soak little enough water that if I change socks I have dry feet, but I usually do not bother because I wear socks that aren't too bad when wet and dry quickly as long as the shoes have a lot of mesh. So it has become an non issue for me, but I do remember having shoes that seemed to never dry.