The difference is there is so much scoring in the NBA that it is rare for a 5 minute OT to not end the game. Double OT games are relatively rare.
In the NHL it would be much, much more common for games to go to 2, 3, 4 OTs. So they would just need some way to make that unlikely.
Something like a 20 second "shot attempt clock" so teams have to play aggressively. Or maybe a rule where if the 2nd OT ends with no goals, the team with the most shots on net in overtime wins the game.
f***, why not do 1v1 60 second overtime shifts instead of a shootout? That would be insanely fun. It would be the ultimate test of skill.