Max
You seem to be thinking this through very carefully and I agree that putting a muzzle on just for garden use could end up with Max not asking to go outside to the toilet if he hates the muzzle. This is a tricky one. Toby scavenges in the garden too, but we have the patio fenced off so he doesn't get unsupervised time in the garden. So it's only on walks where we have been hitting major problems. Incidentally, his poops are "great" now he's not stuffing himself with all the c**p he finds on walks. Toby has got used to his muzzle, in fact it didn't take him long. He does sometimes roll about trying to remove it but it stays put unless he plays with another dog. The only thing I can suggest is that you get Max totally used to wearing the muzzle so that when he goes outside to the toilet, putting the muzzle on is no problem for him. Make putting it on fun and offer treats, especially before it goes on.
I find it a godsend at the moment and the fact that he's not causing himself sickness, diarrhoea or runny poops (and infection) makes it worthwhile but ultimately I want to take him out without it, so working on the "leave" command is vital.