Foam mute--Why didn't I do this years ago?
Because it wasn't a trendy TB must-have, that's why. But yea looke now upon what thou hath wrought--you done gone and kicked-off the Next Big TB Craze: foam mutes! Flatwounds are SO last year, y'all; but if you rush there may still be time enough to jump on the Foam Mute Bandwagon before it becomes passé (again).
And yes, your suspicions are correct--I myself keep a few different foam strips to use when appropriate, which is frankly not all that often. And I have a bass strung with flatwounds, too.
LOLLOLLOL
) Anyway, the good thing about the Patton Mute is it is covered. The cover is something that is picked out by you. Something to reflect you personality/playing. It is not going to crumble away on you like a sponge would. It is also even in thickness from E-G. No messing around trying to get that towel just right. Also, you can remove it easily, no drilling holes or disfiguring your bass to get that sound. 