When building a timeout testing circuit to a non-exit, do not weight as for an exit?

When we're building a circuit to test timeouts, we select our final hop "non-strictly": we try to choose it from among exits, but if we can't find any exits, we are willing to choose a non-exit.

But right now, when we choose a non-exit, we still weight it according to exit-weighting rules. I believe this is incorrect, and we should weight as for a middle.