I would not assume there's any core
rot here as the builder
likely sealed it well at the chainplates. Be careful as you check that you don't introduce a future core leak while checking.
I assume you've checked the chain plate attachment below decks for any sign of rot or bolts pulling out?
At deck level, it is important is to check if there's any sign of crevice corrosion
in the chainplates where the stainless was oxygen starved as it went through the deck. It's best to remove them for this check but depending on deck thickness you can sometimes see well enough. If there's any question, replace the chainplates (and depending on age this might be worth doing anyways).
You could certainly try some new tech solution like titanium but the current
one sure has given good service
for a long time. I'd just replace with the same.
As for the leak that got you into this, I agree with the "use butyl" crowd. The leaks are caused by the caulk not sticking to the stainless chainplate after expansion and contraction has flexed it a few million times. The caulk always sticks fine to the fiberglass deck. As Butyl never really drys, it stays flexible and sticky for 40 years -- so it will move with the stainless instead of separating. Caulks like 4200 will stick for a while but eventually harden and separate. In any case, clean the chainplate well with acetone or other solvent so that there are no contaminants to interfere with adhesion.
But to make Buyl work
it has to be held in place by a plate round the chainplate like in the picture. On some boats these get discarded along the way since you don't need it as much with an adhesive
caulk like 4200. Pack the butyl in and screw down the plate to compress it. The best butyl tape for boats is from MaineSail https://shop.marinehowto.com/products/bed-it-tape