I'm sure that will improve the validity of the scores, though big-picture-wise, I don't like my score to completely reflect the games I tried.
For example, in October, I tried only 4x5s and finished 21st in speed, but had a good points-per-game average. In November, I tried only 4x4s and finished 7th in speed, but had a terrible points-per-game average. Neither "award" was terribly interesting - my skills are somewhere in the middle.
If I were czar, and inappropriately could direct development (obviously, you do all the work and I'm only mentioning this in the spirit of what I think would be nicest for me, me, me), I would have leaderboards for each type of puzzle and difficulty (just speed and totals) and only have one total-points board combining the different types of puzzles. I'd also expand the record-keeping so that we'd always know what our monthly places were, even if we didn't receive an award.
You have to worry about monetization, too, and there are plenty of people here who don't care at all about speed or points.