Before I picked a Group 2, I'd first check to see if a Group 4 fits, and if so I'd get a NAPA 7212, this is a large commercial battery, 1170 cranking amps at 32 deg. F, gobs of power. I've fit these into almost all prewar senior cars with underseat batteries, 40-42 160s and 180s, 33-37 Eights and Twelves thru 1939, so I'd think it should fit your 39 Super. I'm not aware of a higher capacity battery for these applications, and at least in my experience they give very long service life, usually 6-8 years or so.
Height 9-1/2
Length 12-1/2
Width 6-7/8
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