Best thread sealant for exhaust studs into water jacket

I agree with moper... the main problem is the loose threads. IMHO, you will need something that is a medium strength thread locker, like the Locktite 5770 that you mention, or the Permatex product that Lelo Dart cites. (Blue Locktite would be better too but its temp rating is lower.) The traditional teflon and pipe thread sealers are all low strength types, and I suspect will just 'flow' when subjected to these particular conditions; the low strength sealers are just fillers, not lockers, and depend on the the threaded parts fitting tightly to provide all of the mechanical rigidity.... which you don't have in this situation.

FYI... With the medium strength types, they take a day to cure to nominal full strength at room temp and will be stronger if left to cure for several days.