You might try checking out a lawn tractor battery and then using TWO of them (but in parrallel instead of the series arrangement in the MGA). They are only about $25 each and would have a combined capacity of close to 500 CCA. I just looked and a lawn tractor battery size is 7-3/4"L x 5-3/16"W x 7-5/16"H.
I have ONE lawn tractor battery in my race car (Sprite) and it works fine, but probably doesn't have a lot of reserve.
I converted my MGB to a Group 26R battery (from two 6 volt batteries). Works fine but I'm not sure if it has the same size tray as an MGA. The 26R battery is 8-3/16"L X 7"W X 9"H
By the way, I bought my '00 Miata new and it still has the original AGM battery. Still works great! Has never been garaged and is driven all Winter.