I think the idea of a best of three for all PO games is a good idea.  And in the meantime after relegation games, maybe rest of teams can have mini-tournament as deciding factor fora new round of draft picks.
So rounds one, two and three of draft go as normal.  But round 4 would be only for non-playoff teams.  So in other words playoff teams will end up with 3 draft picks and non-playoff teams get 4 picks.
Mini-tournament will be single game bracket elimination all the way through with all non-playoff teams seeded 1-8 in order of standings.  Then can go 1-8, 2-7, 3-6, 4-5 like NBA play-offs.
Just a rough idea, I don't know if it will work.