Cash,
You asked, so here goes.
If you can buy it cheap enough, and the title is right (don't underestimate the value of that), then yes, switching to an appropriate frame could be a solution.

If it were my desire, I'd get either a very solid stock frame and put better suspension and the V8 it deserves, or get an aftermarket frame made for the '34 Chev. There are several companies companies who make those frames, the most experienced is Outlaw Performance http://www.outlawrods.com/ .

Which you choose should depend on your experience or what experience your friends have. Modifying a stock frame could be less expensive, if it's very sound, and you have the skill. Otherwise, you'll be dollars and time ahead buying a professionally built frame, building it up, and swapping the body.

Without seeing the car it would be hard to tell you what the body alone would be worth. If you have to repair ANYTHING (such as modifications the other guy did to mount it to the S10), that's a negative. If you have to paint ANYTHING, or redo the upholstery, those are negatives. The seller won't see it that way (remember, he's looking for another GFT), but after he see's nobody else is willing to bail him out reality might set in. And don't expect to get much out of the discard chassis and running gear. Remember, people who think that this chassis swap is a good deal are basing that decision on the S10 being cheap. And as Streets pointed out, the 2.8 V6 did not have a lot of fans, the 4.3 was way more desireable.

Choose wisely, it'll increase your enjoyment.