Thanks to all your answers. Okay, I'll bite the bullet and buy another pair of cycling shorts. That way one pair can be washed in the evening and the second pair worn during the day while the first pair dries.
Which brings another question: given how slow the padding dries, how do you dry it? Ideally I would like to hang it up somewhere on the bike where the wind would act like a dryer, providing it doesn't rain of course. Do you have any experience with that?