I’ve tried a bunch of Muff pedals and I keep coming back to the EQD Hoof which is a modified Russian Muff with a shift knob that allows you to dial back in more mids. I find that it cleans up nicely when I roll back the volume on any of my guitars.
You might want to look at the DOD carcosa which can do muff like tones but also offers a much wider range of fuzz tones.
Your fuzz face would probably accomplish what you’re doing better if you used single coils. Rolling off the volume on a strat plugged into a FF is one of those classic tones.
Pushing a Muff with a TS pedal is a well known trick but I think I’ve read about it being used more for solos? I think you could get it to work for “cleaner” parts too.