Make it only 5 turns long, skip the debates, and after turn 5 do the general election. Since you are not keeping a card for the debates only hand out 5 cards per turn. Players are then forced to be more judicious with their Candidate card and momentum markers. I would also suggest making a one page reference sheet for the rules so the kids don't have to thumb through the rulebook.
Good idea on the cheat sheet! Also, good idea on skipping the debate.