Everything from around that age suffers with rot so whoever take your Stag will need some bodywork skills. It was heavily criticised for cooling problems and many were fitted with a Rover V8. The fix was a thicker radiator and today you could consider a waterless coolant. But PB knows all that without me wittering on.
My father put a lot of thought into the cooling issues. A thicker core radiator is only addressing the effect, not the cause.
He realised that the auto gearbox filled the tunnel, with very little clearance. This is where air drawn in through the radiator needs to go, to exit at the back bumper, as the air under the car is high pressure when moving. with only a small gap, airflow might be insufficient.
On a dry day, he placed a couple of old oily rags under the bonnet, and set fire to them. They smoulder slowly, and give off lots of smoke. With the roof off, he drove away, with him and brother lookiing for the exiting smoke. There was none. Brother laid over the rear deck/bootlid, but none exiting from the rear.
He found that the air through the radiator, exits forward past the headlamps, to be drawn in through the radiator again. Not much cooling effect from that.
Next stage was to stick bits of wool over the car to determine airflow, particularly around the bonnet and front wings. The bonnet does not reach the front of the car, there being a short deck in front of it. He found the front edge of the bonnet, maybe 4-5" from the front of the car, had the wool standing straight up. So a low pressure area there. Aerodynamics of the car, poor. So he cut two slots each side at that point, relit the rags and off for another test drive. Two lovely plumes of smoke each side, rising about 6" before dissipating. He also added a plate beside each headlamp to prevent the air escaping that way.
If you've ploughed through my story above, you'll know the car led a hard life, lots of amateur motorsport events, a session around Castle Combe racetrack, and driven briskly on the road. No more overheating. Standard radiator.
Another issue is the V engine. Block, heads and manifold are all alloy, but different, forming a triangle, and as they heat up, are pushing against each other. The manifold gaskets get a hard job keeping coolant in with this expansion/contraction, and generally last only around 24,000 miles, so became a service item to replace every 12,000. Coolant leaks into the inlet manifold, drawn into the cylinder, to be expelled throught the exhaust, or dropped into the sump, diluting the oil. Oil pressure is low on these, diluted oil is not good, and the crank bearings have a short life as a result.
He bought the car with 35k on the clock, already with a replacement engine. He reshelled the bottom end and resealed the manifold at around 50k, at which point he performed his cooling mods. Last used at around 140k, needs another engine rebuild, as oil pressure was almost zero again.
Structurally, I think it needs sills, and the front wings are a bit frilly at the wheelarches and rear edge.