Paul,

I'm not so sure that you will get a decent result from that kind of set up, or even a safe piece of equipment for that matter. Trying to resaw a thick block like that with a short stroke saw will be very hard to do because the blade will bind and overheat in the center as the sawdust accumulates. Band saws excell at resawing because they cut down and through the material, holding it to the table and clearing all the sawdust from the cut, keeping the blade cooler and eliminating the lift of a reciprocating type saw. Try a simple experiment to see what I mean, put an 8-10" blade in that HF recip saw and cross cut a 6x6. Let's assume the recip has a 1" stroke, the firt and last inch of that cut will be much cleaner than the center, which will show at the very least the paint that burned off the blade, and at worst the wood will be burned from the friction of all the sawdust clogging the cut that the short stroke can't clear. If that doesn't convince you, try to rip that 6x6 with the same set up. The result will be similar but will require more effort because the blades are not designed for ripping.

If you still want to try and build this machine I would suggest building a giant scroll saw. Binding the blade at both ends will make it safer and more accurate, and by offsetting the fulcrum you can increase the stroke, improving the quality of your cut. Also consider a rotating crank/rod assembly rather than the recip saw as your motor, the reciprocating transmition robs power and adds heat to the system. You won't however be able to easily overcome the lift issue and will be cutting very slowly indeed.

Tom