I suspect you have to keep Newton's Method in mind. Try a bunch of variations on processing time (from normal development to twice the extension recommended for a 1-stop push), plot them, figure out the slope (of contrast and speed vs FD time) and then either interpolate or extrapolate to get the right answer. Then test again with a few points clustered around where you expect the right answer to be.

And then deal with the fact that 5+ sequential processes (assuming rotary or inversion) would oxidise the developer somewhat so maybe consider single-shot development for this testing to avoid that problem, but keep all the once-used developer to go back into your main stock for use on real films, because the single-shot won't have harmed it much.