Randomly generate paths with a given length and surface coverage

I am working on a tower defense style game where I want to randomly generate the paths based on given criteria - specifically the length of the path and, if possible, how much it doubles back/stays in through the same area (or in other words how much of the path a single tower could cover).

In practice, the difficulty of each random map could be controlled by the two parameters (shorter length is harder than a longer path and a path that's more spread out is harder than one that's compact).

One potential solution would be to look through every possible path from the start to the end then curate it based off the parameters, but I was curious if anyone has a more optimal method or idea that may be better.