Ideally, you need a new radiator. the 53 item will only be rated for a max pressure of around 7 PSI, and a 350 engine works best with around 14-17 PSI. Since the cooling system boiling point rises 3 degrees F. for every pound of pressure applied, you're going to be riding the ragged edge of disaster anytime the pressure spikes a little during warm-up, even if the engine doesn't actually overheat.
If you're willing to get a really professional cleaning and rehab of the original radiator and add an electric pusher fan in addition to the engine-driven fan, you might get away with the original low pressure unit. Personally, I wouldn't bet the farm on it. The smaller hose nipples on the radiator can be addressed by slipping a short sleeve of radiator hose over the nipple, then using a larger-diameter hose over the sleeve. Put the adapter sleeve on dry- - -no sealer of gasket goop, and use a good-quality worm-drive hose clamp to hold the whole assembly on. I have used that technique on racing radiators with a 21-lb. cap without any issues of blowing hoses off.
Jerry