Those tires are the culprit here. You can fit a 275 wide tire in the rear of a 69 no problem. You will not need upgraded axles with the automatic trans, as that combo doesn't shock load the rear axle as bad as a manual would.
Also, 1st gens are notorious for axle wrap and wheel-hop due to the leaf springs. They sort of raise up in the rear when launched, instead of transferring the load to the rear and squatting a bit. Get yourself some Cal-Trac or Slide-A-Link bars, they work wonders for leaf spring cars.
I had one of my 69's running 10s, with Cal-Tracs and drag slicks. It hooked excellent.
It wasn't even a drag car, it was a pro-touring car with just a tire swap:
http://www.fquick.com/garages/Chevro...o_SS/1969/232/