Blossom EndRot

I wonder if the pH in that spot is off. Perhaps that would explain why your remedies didn't have
the effect you expected. The soil test would confirm that, although by now, perhaps the Epsom
salts have adjusted the pH, thus masking the root cause....

Just thinking out loud on this one.....

Have you had any indication of significant calcium deficiency from past soil tests? While calcium deficiency is ultimately the cause, it is a deficiency within the developing cells of the fruit, and not nescessarily a deficiency in the soil. You can have plenty of calcium in the soil and still have rampant BER.
What often happens is the plant gets too much water...the calcium in the water is dilluted, the water is taken up and delivered to the developing fruit, causing rapid growth without adequate calcium to allow proper tissue structure.
Often, fruit growing during rainy periods may have BER, while subsequent fruit may not be affected at all. Repeated drying/wetting of soil is especially bad. Calcium delivery is limited by the lack of water, then when the plant is watered, it rapidly takes up water to rehydrate cells faster than the plant can utilize and efficiently deliver calcium.
As you probably know, some fruit types are much more prone to BER than others. I don't recall the explanation, but plum types and paste types have more tendency to get BER. Beefsteaks are less prone to it.
In general, relatively dry soil is good for tomatoes, as long as they're not allowed to repeatedly wilt.
Epsom salt is often said to reduce or prevent BER, but I think this is more myth than fact. Epsom salt's main value to plants is the magnesium it provides. Magnesium is usually only a recommended amendment when it is deficient in soil...as it's a trace element, it's often adequate in soils with loamy organic content. There have been claims made for the benefits of epsom salt forever, but little substantiation for those claims.
Also, don't believe the claims for products like StopRot, a solution of calcium sulfate used for foliar application.
Others here could probably correct some of my statements, but this should be fairly accurate info.

TY both. I'll keep amending the soil and have it tested next spring.
It's an abominable garden plot at best, but this is only Year Two of my correcting the evils done by generations of another family.

So if it is distribution of water in the garden, would making raised beds for those few varieties help?

Or should I just continue with my soil amendment (addition of leaf mold), low tillage and possibly a green manure?
I always rotate crops so they won't be in that section next year anyway.

Raised beds always help. Just mound up the soil into a row where each row of plants will go.

Well, thats the thing about raised beds...you dont NEED to till. Maybe just a little turning over of the soil with a fork is all i do. I am a big proponent of raised beds for sure.