Here's your "modified shootout".

5 minute overtime starts with 4 on 4. Each minute, both teams have to remove a player.

5 - 4 on 4
4 - 3 on 3
3 - 2 on 2
2 - 1 on 1
1 - goalies duke it out.

I actually like the idea if there were a good way of removing a player without stopping. Not sure how that could happen though.

Guys come off for line changes already - give them a 5 second grace period and if they violate it make it a 1 minute penalty and drop the puck at center ice.