I think I'd prefer the giveaway way, like is done on Steam Gifts. Let people sign up for the giveaway over a period of time, then they'd have a chance to win the game based on how many entered and how many copies were made available. This would both limit the number of copies but not limit the time period in which to enter, and doesn't penalise those who are slow to enter.

The only fair thing to do is to distribute the game randomly. The publisher gives GOG 30k copies of a game? Then distribute them randomly among GOG users. The only thing we have to do is praying to the RNG or our deity of choice.