Some have run long hoses. I ran into this with my 65 Dart 273. The radiator had been kissed by the fan and ruined. The only radiator I could get at Autozone was a 71+ square-top w/ lower hose on passenger side. I swapped to a matching alum water pump since $30 vs $65 for the cast iron original, plus seemed smart to not form the steel-alum-steel "battery". I installed a later timing cover since mine was almost corroded thru.
Problems: My TRW power steering pump bracket didn't fit the new water pump, so bought a later Federal pump and brackets. The alum water pump is 1" thicker, so couldn't fit the new fan/clutch. I had to cut a timing mark in the damper for the new tab. I had to play with pulleys and belts to get accessories to work, and haven't gotten to an AC compressor yet.
In sum, it might be easier to get a correct radiator. Yours doesn't look like A-body anyway, unless 71 or 72 still had the round top. I am guessing it is a B-body, and those are usually slightly too tall to close the hood, so did someone make mod's to work? Before buying another, consider if you will have AC, so the top hose location isn't also a problem.