how about giving some health after beating the level, like 10% and more if the player managed to beat the level within certain amount of time? It would reward the player for playing the game more aggressively.
The end of the level would be a good place to reward player but I'm not too keen on using time as the condition. I have so far intentionally avoided all time limits and time rewards. Also, determining the actual time limit for the reward would be tricky because the levels are procedurally generated and unique.
Someone suggested simply restoring the health to some minimum value on level completion/start, so that the a level would never start with near-zero health. I kind of like this idea but perhaps I should limit the total number of times the health would be restored.