After much consideration, I think I've arrived at a solution. I believe that a long rest should be followed by an 8 hour cool down. The player should be forced to exit the game for the next 8 hours. This will make the choice to long rest something the player has to seriously consider.

In addition to this, I believe the short rest should be followed by a 1 hour cool down. If the player doesn't want to exit the game, maybe the screen can show the camp fire for the prescribed amount of time while a bit of soothing music plays.

All of this will bring a much needed level of gravitas and immersion to the resting system.