Is there any way I can get a good Jimi Hendrix/ Tommi Iiomi(?)/ Neil Young fuzzbox sound using only a TS-808 and my valvetronix amp?
Not really, especially into a modelling amp as they don't respond well to pedals (though the Valvetronix are better than most). Whack the level and tone quite high and keep the drive fairly low is your best bet
Unless you break it, it won't even get close. My advise is to either roll down your tone control on your bridge pickup, go to your neck pickup, or both.
Don't know much about the valvetronix, but i'd imagine they'd have some stuff built into it that would let you get that tone without a pedal.