Why don't you check out where the laundry (or laundries) are at FW before making a decision?
At CBR they are beside each quiet pool, so while we're running through a few loads of laundry, we're also sunbathing or splashing in the pool....sure beats going offsite to who knows where for who knows how long.
We've even done this in the evening - the pools are open (and heated in December when we travel to WDW), so we splash around to our heart's content while our laundry is doing its thing. And we're doing laundry for 2 adults and two large teenagers, so it's usually a lot of stuff.
At least at CBR, if you don't overload the dryers they dry clothes quite fast.