I think I know the answer already (it will be: "because f*** you, that's why"), but is there any way to change the setting so the season games happen when I'm awake and not always between midnight and 3 AM?

With the glitch in the generation of championship games it messed the times around so hopefully next season this will be at a more convenient time for our American friends.

Nope, still between midnight and 3 AM.

Can't really tell my friends, "Come play this game, you won't really get to play, just click a couple buttons to assign stats."

Your level is what matters here. Since there is no glitch this season, Randy, you must be under level 11 (on this account). The prime time, PM, is for upper level teams and the lower levels mostly get the AM. But it has been this way so you must have gone through this before.

Actually, I made a post about this exact thing not too long ago. I'm with you 100%. It seems looking at the live games that are going on and judging from my own guild and when their is the most action happening, there is indeed a prime time window. I also agree that the higher level championships should be more in that prime time window and some of the lower ones (that no doubt end up being robot vs. robot match ups) can take place at that 3 AM time slot.

well, if I want to play at 6 AM (GMT-5) what's my target rank?

Your target rank is always as high as possible- your stat cap grows as you gain rank, so choosing not to rank up actually hurts your team in the long run.