I am rather fond of lawn mower/tractor batteries and the battery and cords and all fit in a utility box.
https://www.homedepot.com/p/Interstate-Battery-340-CCA-Tractor-Mower-Battery-SP-40/205754489
Currently, you can carry them on within the guidelines.
https://www.faa.gov/hazmat/packsafe/more_info/?hazmat=7
You definitely can't have them in your luggage or ship them as freight - and the fines are significant.
We have a smaller carry-on pelican case that has slots for about 16 lithium instrument batteries but our base batteries are all AGM so they can be checked or shipped air-freight.
Shelby's link to the battery appears to be munged, but I think this is the one he's talking about:?ÿ Bio Ennopower BLF-1220AS.
The link probably doesn't work because the original post is over 2 years old.?ÿ Still a valid question though.
I travel a fare bit for work and usually have a bag full batteries but I'm guessing they will freak out if I have a large base battery to boot. I think there is actually a limit to the size you can carry on. This also causes a problem with the new lithium version of the Leica brick batteries.
Ps where did you get the case?
I didn't go through all the replies but I figure ill put my two cents in. Had same problem with batteries ultimately we switched to optima batteries and it made all the difference. There not cheap but we get all day use out of them as well as they are lasting?ÿ 3- 4 years! Not bad for a battery that's getting charged every day or two.?ÿ