for polyphony you need a separate signal for each string. never seen the spec for the 13 pin style pickups but there has got to be one somewhere b/c there are multiple brands and approaches
it sounds like you want it to fit into a standard form factor so i would look at maybe making a low impedance coil around each pair of mags on a jazz bass or something like that. you can get 13-pin jacks that mount in a gibson les paul style side jack plate. probably have to get that from roland. from there all you need is a 4-channel pre to get each signal to the level and impedance in the spec
BTW you do know that there are kits for installing a GK pickup in a strat type guitar that use the 13-pin jack instead of the bolted-on enclosure? there is this
GK-KIT-GT3 GR-Synth Driver Kit: Shop Accessories & Other Musical Instruments | Musician's Friend plus the graph tech system which is even more aesthetically transparent
personally i wouldn't think it would be worth the time just to save money. you can get GK pickups and junky old roland guitar synths on ebay real cheap. even without figuring time you won't save more than a couple hundred bucks on parts over buying old GK stuff. plus a whole team of really smart japanese engineers has solved all the same problems that you will encounter...
there is a roland gr-9 on ebay right now for under $169 - that would give you midi out that you could run into your regular midi interface on your computer, plus some foot controls.
http://media.rolandus.com/manuals/GR-09_OM.pdf then you just need a cheap used GK pickup
if you really like the idea of hacking you're still better off starting with a commerical product. get the gist of how it works, hack it, and if you come up with something you like a lot better you can start on your scratch build from that point.
i just don't see a compelling reason to DIY for what you want