Is there any relationship, other than pure coincidence, between this
naming scheme and DEC's F, G, and H floating point number formats?
I don't think so. The System/360 letters referred specifically to the amount of memory available, so a D compiler would run on a D machine with 256K, and E/F/G were 512K/1M/2M.
The DEC floats were an extension of Fortran's exponent letters: D=double, E=generic, F=single. G is a variant of F with a different mantissa/exponent balance, and H is double double. S and T floats came later and were bit-for-bit compatible with IEEE binary32 and binary64 formats. Lisp went a different way: to D, E, F they added S for small floats and L for large floats.