You don't necessarily have to put an extra game. Maybe the offseason should be reorganized so that games 2 and 3 of the final playoff do not fall on consecutive days?
This might be an annoying wait for teams 4 and 8 in the rankings, but there is a way to work around this by organizing a bottom 4 playout bracket:
Game 1: 5 vs 6 and 7 vs 8 (possibly cross-division as it is now)
Game 2: Winner vs Winner and Loser vs Loser
At this point, the team with 2 wins is guaranteed to avoid relegation, the team with two losses is relegated, and the teams that split a win and a loss play a 3-game series to determine the second relegating team.
"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve."