I just run a piece of wire with about .5 inches stripped off, and lay it underneath the bridge, between the bridge and the lid, then clamp the bridge down on top of it.
almost every electric guitar is made like this, Fender just screws a metal bridge down hard onto an exposed wire, Gibson bashes in a threaded metal insert for the bridge post to screw into over a bare wire.
in my opinion it will be very difficult to solder to this screw as you say, how will you turn the screw afterwards to drive it in without breaking the solder? you can just strip the last inch of wire and wrap it around this screw or if you really want to be completist there are little terminals for auto electrics you can get cheaply which will end with a ring like a washer, but having a tab you can crimp onto some wire, you'll get a bag of a hundred or so at the auto parts store for a few bucks..
Cheers guys for the responses, its all clear to me now!