Hi LTD-HP and welcome to the Forum!
Firstly congrats on your 310!
I refurbished mine, and learned some stuff along the way, and I am not the first!
Its not rocket science, and yours maybe similar.
Mine did not need a new core yet, I did do some research and found some inexpensive replacement cores that would fit..
You could make a U pipe to bypass it while you are fixing it, but many others have clamped off the pipes, or added valves with no ill effect I read.
While you are there its common for the 3/4" pipes to and from the Auxillary heater to need replacement... I heard that there is about 70', unless my memory is wrong... I have not got to that bit yet!
Anyway, here is my thread on the matter to get you started!