Got a perfect clear with no orbs used. I suspect it’s 80% early dumb luck, 10% early rat king and 10% strategy. Plus the rat king revealed the eventual location of the bomb scroll as the other corners had rats in them. I think detonating all the bombs as soon as you get to 10 hearts is an important step to a perfect clear.
One strategic insight is that it’s best to start with the squares around the dragon, as they’re more constrained than everywhere else. One has to have the egg, and the squares that are directly North, South, East or West of it can’t contain 7s. Essentially that means if you click all the squares around the dragon and clear them, you’ve probably got a good layout for this challenge.
Early on you’ve got to expand in whatever direction you have good information for, and I suspect that if this goes in the opposite direction to the King Rat area then it might be best to restart. The rat reveal is essential for two reasons: 1. The rats give you much more flexibility in using up your hearts, 2. The information you get from killing them is even more useful in this run where you’re very constrained by not using orbs.