You’re right that the NHL will never do anything to fix this.
But never in the history of the salary cap era has there ever been a player who was legitimately injured at the end of the season and for reals recovered just in time to start the playoffs. Every single case has been cap circumvention.
So, I like the idea of setting a second deadline after the trade deadline. Maybe a week prior to the end of the regular season, all teams must reactivate any players who’ll be taking part in the first round and become cap compliant.
Any players not reactivated from LTIR by that date won’t be eligible for round 1.