A UK company called Nova acquired the machinery and rights to manufacture Avon tires. They have indicated CR6ZZ tires for Cobras and GT40's will continue.
Don't think the site is gone. Frequently there are temporary shutdowns or difficulties in bringing the site up. This has been going on for a few years now.
Agree that the repair is worth a try. I'm not optimistic you're going to get the balancer off and back on with SPF clearance. Also towing the car and having the engine removed is way more complicated.
I would agree with Lee's advice Mike. Yes the waterpump can be removed with the firewall off and serpentine belt removed, but best to determine what if anything is causing overheating. Weeping from the waterpump would not cause this,
My advice is find out about registering a replica car in NJ first. NJ appears to have difficult laws about replicas. I assume you're considering Superformance? If so contact the NJ dealer:
https://www.jonathanmotorcars.com/
Yes the block code would be modern. They are built with new Dart 4 main blocks. Getting an engine built with a 1960's block will be difficult especially for the power output you want. It would help to know what state or country you plan to title in.