yea, 13 hearts is the max possible. I've used the cheat code to confim it in the past
I don't actually know the cheat code, but I manage to get 13 hearts left pretty regularly. One key is to take the risk and die (often) rather than take a heart and accept a lower score. The really tough bottleneck is this one point where you are just one diamond short of leveling and you almost always at this point need to get lucky multiple times to get the Gnome.
General strategy is that you have to be aggressive in exploring the map while conserving health, which often means taking a risk rather than playing it safe. If you can figure out places where all neighbors are definitely non-zero, that's good. It means the Gnome can't escape to there. So try to explore in other directions, and don't take the health hit.