I understand your pow and you are right: the abbreviation "MiniG" it's not a good idea

For the other words (you have right) maybe inserted, but I think it's impossible to have a good (clear) picture with little dimensions (I think about 16x16, 24x24 and 32x32): in my intention, I tried to find big and little logo picture compromize.
For this reason, my first idea (very simple) contains only the three letters "HMG" (project name) and I (re)used the same colors (yellow and red) to remember it

Of course, HMG can have more then one images

Bye