That's why I have multiple basses. My 1970 alder/rosewood P has the weather strip mute under the bridge cover, and my 1975 ash/maple P does not. Flats+pick+mute (especially over-string mute) equals instant 60s bass tone. It's nice to have one bass set up like this.
And even with flats and foam mute, it still sounds brighter than the distinguished forum's beloved mudbucker.