Leaking bathtub from seal underneath around drainspout
"The underside of the tub appears to be sealed with some sort of black sealant"


No, that is just a black rubber washer which acts as a cushion against the rough cast underside of the tub. The seal is provided on the top side by a bead/layer of plumber's putty.


"Can I just epoxy that area to stop the leak"


No, you need to unscrew the strainer from the tub shoe from the top side, pack a bead of plumber's putty around the strainer lip, and screw it back into the tub shoe.


"does the tub underside need to be resurfaced, or does the tub need to be replaced?"


Hopefully the tub does not need to be replaced. Assess any corrosion or damage to the drain hole area when you remove the strainer from above. Ususally there is a bit of surface rust but nothing that would prevent a seal with putty. I have seen old pressed-steel tubs (as opposed to cast iron) with pretty bad corrosion in that area.