I wonder how possible this is, considering the original algorithm allows you to use less nodes. I wonder how much that might inflate the numbers, or alternatively how much requiring you to use all the nodes might make ceritian configurations impossible. have you tested it? (I know you tested the original version)
Here's the solution for weak tree(3) that helped me find a similar solution in my game: https://math.stackexchange.com/questions/3837501/before-the-current-lower-bound-... (Oh, and I should also credit my younger brother, who told me about this problem in the first place. He was already familiar with this solution, which helped me test the game initially.)