So today I used the near-styrofoam** and there's enough room. **It's not open foam like styrofoam but a bunch of "plastic" spheres 1/2" in diameter. all stuck togeher. But it doesn't spring back.
Also, Firestone was open and they sell Interstate Batteries, and they had the very same model I have now. No handle. And room for the Battery Buddy. At first I didn't know where to buy Interstate -- thought it came from one of those autoparts stores -- but their very good webpage shows about half Firestone and a similar number of independent mechanics. P.S. The height dimension includes the posts!!
Tomorrow will be colder.