Your plants may be sufferring from too much "goodness". It sounds like you have planted them in almost complete compost with some fertilzer added. That may sound like a great thing, but it isn't. They are probably getting way too much nitrogen, which basically results in foliage and not much fruit.

I would try 1/4 compost with 3/4 regular soil. You can add perlite or vermiculite (or even some sand) to lighten the soil in a container.

Understanding that the growing season is well underway, I would try digging up a 12" ball of roots, shaking off some of the soil (but not thrashing the roots) and replanting them in a more standard soil mix.

As an alternative, you could mix a few containers with the 1/4 compost and normal soil and stick a stem cutting in it. They root pretty well and it is weeks ahead of new seds. You will get a late harvest, but some is better than none.

Your precious pots are wasted on Early Girl. The fruit from that vine is the poorest in taste of any cultivar I can conjure. Yet Early Girls are easy to grow and offer high yield... so there is virtue in that EG can serve as a "canary in a coal mine" that is your garden experiment.

IOW, if EG won't perform in your pots, then nothing will.

I am a big believer in soil, and I break all the rules by growing my toms in almost-all compost and a little "old soil"

I have never used lime... though it has been suggested as a countermeasure to our horrible native soil... which is hard-pan clay. Mostly, I dig the clay out and dispose of it. That's "back breaking" work that is just a way of life for this suburban So. Cal gardener.

Hardpan is common in the coastal area where I now live. In foothill areas (such as Glendale where I lived in my former life) there was no clay.

Your soil may vary! Use common sense.

If you're getting flowers, you're on the right track... for soil. That's my simple rule. Then it's a matter of pollination and fruit setting, to get toms. If you've dumped and reinvigorated the soil in your pot before starting your plant in the spring, as it seems you have, your soil should need little attention during the growing part of the cycle.

Never use the same pot-load of soil twice. Always dump and recycle.

I don't know what the eggshells accomplish. I tried that and noticed they never decomposed. Yes, I know you're trying to infuse calcium... thereby avoiding BER (blossom end rot). I see BER more commonly in potted plants... especially in my San Marzano paste toms... This is a soil-chemistry problem... and can manifest from "too much" water.