Holy convoluted and unnecessary, Batman!
No points are awarded for a tie at the end of regulation. Instead, we go to an OT PP dealy.
A two-minute 5-on-4 for each side. A PP goal would mean the end of the PP, just like in regulation. If one team scores on its PP and the other team doesn't score on its opportunity, that's two points for the former and zero for the latter, game over - unless the team that didn't score on its PP opportunity scores a shorthanded goal. (Shorthanded goals have the same value as PP goals, except they don't end the other team's PP, just like in regulation.) If both teams finish even, we go to a second round.
Now it's a 5-on-3 for each side. Again, winner gets two points, loser gets zero. A tie would be the final result, with one point awarded to each team.
All goals would contribute to the final score. So, a game that's 3-3 after three periods could end up at 5-5, or as high as 7-7 (each side scores a PP goal and a shorthanded goal in Round 1 and Round 2).
I have to figure out what to do about penalties.