I do the same type of thing. I soak mine in water and a little Dawn detergent, rinse it, put it in the microwave and heat it up to kill any lingering virus in it. Then, I take it out, put it between folds of towel and press down to get most of the water out. Then, a one minute cook in the microwave dries it out.
I have about 5 in rotation. Once I steam clean one, I put it in the back of the line. It maybe 10 days before I get around to using that one again.