I'm a heretic. Climate battery is a gross misnomer. I designed and built a home with 2 foot of rock storage below the slab, with massive 600SF of hot air panel in a steep south roof circulated below slab, to avoid air quailty issues which all solar rock storage systems had. I insulated the stem walls with foam and foam skirt, but didn't put foam on the bottom. I had sensors buried at the bottom and top of my rock storage and monitored it for the 20 years I lived there. The earth is a endless heat sink by conduction, so without continued hot air input, in just 3 days it was gone, even if little or no house heating was required. (House had massive passive solar gain also.)
So while moist dirt can be used for thermal storage, unless you insulate the bottom and full sides of the storage area, it will be attempting to heat the planet. You earth temp in MA will be in the low 50s...and is a virtually endless heat sink at that temp. Yes, you can store some heat without it, but a dark stretch of 3 days or more will require supplemental heat.
The glazing losses are horrendous, so I'd rethink the design to have thermal shutters for the south glazing, and no glazing at all on the roof, preferably an R60 roof. There's no need for ceiling/roof glazing in Mass for a winter greenhouse, it's all loss and no gain. If the outside thermal insulting panels/shutters can double as hinged reflectors to increase the gain from the south facing glazing, all the better.
If you do some digging online, you will find that what data there is for hoop houses with very expensively done GHAT with deep side insulation into the earth shows that in just a few days without sun they are dipping into freezing. This is from losses from glazing and into the earth. Both are huge, though glazing is worse.
Save the money you thought you'd spend on Ghat, put it in insulating panels to cover your glazing at night and dark days. And add some ventilation to reduce winter overheating or if want to do solar heat collection and storage, and insulated water storage tank is far more effective. The thermal storage capacity of water is huge compared to dirt.
It's been proven for a small greenhouse, with good data collection by a retired engineer, now deceased. He collected excess heat via air to water heat exchanger and used the same to distribute the heat as needed at night. By not having the tank in greenhouse, and insulated it well, higher temperatures and thus more energy can be stored. Exposed barrels do the same thing but with limited capacity and only low temperatures.
As I said, I'm a heretic. But I got that way after operating what is essentially the same as GAHT or climate battery without insulation on the bottom. It will work as a modest short term storage system and a vast reservoir of mold and bacteria. It's NOT a "climate battery", more of a short term capacitor.
Best Wishes,
BruceM