1976 XJ-S with potential engine problem

Hi Forum members.
I recently purchased an inexpensive 1976 XJ-S in silver grey. The car has been dry stored for many years and the body is immaculate. One owner, and 60k miles in the clock. The interior in red leather looks great too. The only problem is that the first owner admitted that the car had overheated on long trips. I’m trying to decide the best way forward with this info in mind. The car has been stood in a garage for a significant time, so that could explain the slightly rough running, bad petrol etc… or it could be evidence of major engine damage. I can see that when it gets warm on idle, coolant is released from the bleed valve. I’m thinking to start with a compression test to see if there’s significant variation indicating a blown head gasket, and if that’s ok, spend some money and swap the rad out to see if that cures the coolant loss and keeps the temp gauge at normal. With compression issues ruled out The rough running could be bad fuel, or a fault within the fuel or ignition systems which I can deal with separately. I do have a spare engine from a 1979 car but I’d rather keep the car as matching numbers if possible.
Any advice on best way forward would be appreciated.

Step 1 should be to pull the radiator OUT and have it serviced by a rad shop.

Thanks Kirby, I’m hoping the engine has not suffered. Great bible by the way, had my copy a few years now.