Market the GOTMs more. Although there is a good bunch of folks playing GOTMs, I'm surprised that more people don't play them. I've tried to plug them here and there on the Strat forum. Why not just make a sticky thread in the strat and general forums about GOTMs - what they are and why you should play them.
FWIW, I didn't play the civ4 games because I couldn't be arsed to install and keep the HOF mod up to date.
I don't really care how I do compared to other people, other than as an interesting comparison, and I generally play civ with the goal of playing each turn as quickly as possible. Forcing players who wouldn't cheat/reload in the first place to jump through extra hoops is reminiscent of DRM in games which causes extra work for all the non-pirates.
So, I deal with the GOTM (by not playing) the same way as I deal with games with DRM which is too much hassle (also, by not playing).
I've even played a number of GOTM games without the HOF mod, but obviously, this prevents me from submitting them.
I'm not saying the HOF or similar mods shouldn't be required, just giving my take on why I don't participate more often.