Definately ditch the Zoom.
I can get incredible tone out of my mutant strat (again, with noisless vintage single coils) and a XXL distortion box into a good tube amp. You've got a good tube amp, you should be able to get awesome lead tone. Another thing to check is your amp cords. A crappy amp cord can make for all kinds of noise. Also, your guitar may have less than adequate sheilding and grounding, you may want to look at that.