I hate to say it, but you should just leave it alone. There's no reason to bend the MPC-1 for distortion or tone bends that could be done with effects pedals or digital signal processing. If you want more control over the drum synth aspect of it, you may want to send it off to Circuitbenders and have them do this piece on commission. I can't speak for them, but I'm would guess that they'd be able to figure out how to modify the circuits to have it do what it was never meant to do. Some of the vintage gear out there is too precious to bend. Modification using true theory electronics knowledge is the way to go.
I have no knowledge of the MPC-1 except that it is not a part of the MPC sampler line. MPC in this case stands for the Music Percussion Computer, whereas the AKAI MPC stands for Music Production Center or something like that. But I would think that with any vintage stuff, you'd want to have the ancient solder reflowed, the power supply serviced, the circuits re-capped (new capacitors put it), the knobs and contacts cleaned, etc.
You may want to consider MIDI control if it doesn't already have it. I'm sure that if you were really into the idea of modifying the hell out of this machine, you could MIDIfy the knobs. HighlyLiquid comes to mind.
http://highlyliquid.com/midi-decoders/I would also think that you could build LFOs to control all the synth parameters. That would take some electronics knowledge and equipment, but if you could somehow turn this synth into a modular drum synth, that would be super cool. Plus, you may be able to actually save some money over buying prebuilt drum synth modules.
I don't mean to discourage you, but to me, it would be like saying "I wanna fuck with the guts of this rare Model A Minimoog to make it sound more distorted and maybe make some weird sounds". Yeah, you might find something interesting, but not interesting enough to risk fucking up such a rare dinosaur.
If you want to make some weird, fucked up sounds, get a PCM drum machine like the Alesis HR-16/Roland TR505/TR626 or any of the Boss Dr Rhythms that crop up on eBay for relatively low prices, and bend the hell out of that.