I am tinkering with a puzzle framework that has the following rules:

In a 6x6 grid of squares, arrange 8 strips of connected squares such that there exists exactly one strip of every length (i.e. a strip of 1 square, 2 squares, etc up to 8). Strips cannot double back/form 2x2 blocks.

I intend for the clues to be endpoints of said strips, without indication of length. The idea being that the solver is trying to pin down path and length together. Giving all endpoints though is over-constrained and makes for fairly easy puzzles. I'm trying to (systematically/programmatically) shave off information to make the puzzle interesting but still have a single solution. Here are some example solutions and their unsolved over-constrained "prompts":

Any guidance, reading, or other direction would be greatly appreciated.

P.S. Don't hold back on the math, I'm here because of a mathematical curiosity.