The letter codes are indeed Quick Call 1. Quick Call 1 is similar to DTMF where the 'A' tone is a combination of two tones and the 'B' tone is also a combination of two tones.
With the old Motorola QC1 encoder the dispatcher would push the top row buttons with the first two letters then the bottom row with the last two letters. Here's a video of one in action:
What about the A, B and Z groups? When a customer ordered a QC1 encoder Motorola would fill it with reeds from one of these groups. The reason to have different groups was to prevent interference from another co-channel user also using QC1.
Looking at the Wiki we have Booneville FD with a QC1 code of HM NF. This decodes as:
602.6+912.0, 1011.6+489.8 (Group A)
or
623.7+944.1, 1047.1+507.0 (Group B)
or
582.1+881.0, 977.2+473.2 (Group Z)
Unfortunately the Wiki submitter did not indicate which group is in use so you have a 1 in 3 chance of getting it right.