350 horse out of a 273 is possible, but going to be a bit of a stretch at 1.28+ c.i./h.p.- and will take more than a distributor and headers. And when a motor that size is pushed to those power levels, it's going to get finickier and finickier...
They are fine, fun motors for a street cruiser, with enough spunk to get the job done when called upon; just don't get carried away with horsepower expectations. Even the special order 1966 "D/Stock" factory race Darts were "only" putting out about 275 horses as delivered...
IMO, a mildly upgraded Commando/Charger motor (which is what that engine appears to be, although the cam may be a hair large for your average cruiser 273) will meet all your expectations on the street- just don't get too hung up on HP numbers.
As far as sounding nice, the Commando/Charger 273 engines had one of the best sounding exhausts ever engineered- and it was a single!