A solution could be, extend the game by whatever power plays are called with right of refusal.
I've been beating this drum for awhile. Name one other sport that increases the standard for what qualifies as a penalty in the final 2 minutes while also reducing the consequence for commiting such a foul.
For example, imagine if the NFL decided that they'll now allow Pass Interfence and Roughing inside the 2 minute warning unless it is the baddest of the bad. And even then if they do call it, that the penalty is reduced to 5 yards instead 15 (or point of incident with PI). Furthermore, if you commit a penalty preventing a touchdown on the last play of the game, it's all good, we'll just give you the penalty on the box score, but since there are zeros on the clock the other team doesn't get to execute a play after applying the penalty.
If they did that, everyone would lose their minds at the stupidity of it. Yet, this is standard practice with hockey.
Or in soccer, if you commit a foul in penalty time that results in a penalty kick, imagine tthey make you take it 20 yards further back or not at all because of the time.
Or in basketball, say they made fouls inside the final minute now only result in a single free throw instead of two and if you commit a foul on a player on a buzzer beater, no worries.
This is what we're told to think is reasonable in hockey. Frankly, it shocks me there aren't way more incidents like these in the final 30 seconds of a 1 goal game.