Agree with you, just saying because I'm seeing a lot of effort on flames, like the lines of code from @kn0w0n3. But for example, nobody talks about why that kind of creeper plant is holding the queen while it melts... Maybe applying maths, logic and counting is not the way for this one. Take this only as thoughts, I really admire all the work being done here. (And in previous puzzles that I followed too).
I don't think it's been mentioned before, but the vine seems to originate from a single white square on the bottom row.
yes it has been mentioned before (I can't find who mentioned it though, you would need to read through the thread to find it) that the vines grow NOT from tiles but from the cracks between tiles, the same about the key hole - it is between the actual tiles. I have this idea that didn't bring fruit yet, that it is not tiles that count but the so-called (in mathematics) lattice points. Lattice points are points where the cracks ("grid lines", as wikipedia puts it) intersect. In that case we would be dealing not with 7x9 chessboard, but rather with a 6x8 lattice, but the key hole and the growing vines could be expressed by integer coordinates in the lattice.