Fur"face" help

If you check around online, i have seen some places that make latex prosthetic muzzles/snouts, which can be attached with the usual cosmetic adhesives and then painted with makeup to blend into your face. It wouldn't allow you to make your own muzzle, but it's an option.

Alternately, if you made the harness out of something porous, like mesh, or thin but strong, like fishing line, you might could strap the muzzle on and then comb your hair over and through it, to mask the straps. That's what i always do when i wear my horns, anyway. If you had a top strap running through your mohawk, you could even try adding some fake hair/fur to the forehead section to try to blend it right into the muzzle.

I suppose another option would be to try molding your head very closely to make a helmet of sorts--a hard-shell apparatus that holds together with a plate on the back your neck and supported itself with two plates that cover the sides of your head and rest on top, leaving a channel for your hair. Basically, you'd end up with a fursuit head that's missing half the face and a big swath down the crest of the skull. You'd need to mold it pretty closely, though, and probably add a chin/neck strap and maybe a set of head straps underneath, like you see in hard hats, to keep it from sliding around. And i have no idea if it'd actually work.

Spirit Gum. I used it for my Last halloween costume.
It can be quite effective...seeing how I glued my sister's ass to the toilet seat for April fools. Sweat can cause the Adhesive to weaken over time.

Get a pair of glasses, cut the lenses about, and just use the bits that go about your ear and build the muzzle on that? Second option, have elastic loops that go around your ears.