No more trouble than changing a stock water pump I'd guess. You'll probably have to re-gasket the water pump spacer at the same time. There is a new pump spacer available with a beveled edge inside for better flow. (last photo)
Is the Temp gauge showing on the hot side or is it actually spitting coolant out past a good radiator cap?
The gauge can easily be incorrect, double check the engine temp at the back of the thermostat housing with a heat gun from the hardware store.
If the 60+ yr old rubber diaphragms in the double-sided vacuum canister on the distributor have a leak in either side or the points plate is stuck the timing won't advance properly and cause overheating.
https://www.ctci.org/cracked-exhaust-manifold/
More overheating causes...
https://www.ctci.org/1955-56-57-thun...d-overheating/
general Baby Bird tech info....
https://www.ctci.org/gilsgarage/
After all these years one of the bigger causes of overheating is sediment in the water jackets. (first 3 photos)