A nice idea but the flaw would be in the quality of the non-control predictions based on a past-life analysis because there's no objective way to know that you're really drawing predictions by analyzing a past life vs. tapping into someones imagination.
The obvious problem is knowing who (or what) the alleged past life was, let alone the sexual orientation. There would be no experimental difference between a prediction and a guess.
From a scientific perspective, the result would be comparing guesses with guesses. I suppose if you ran the experiment enough times to generate a statistically significant result set, you could draw some conclusions.
For example, if the non-control group *consistently* scored highly compared to a random distribution in the control group then that would suggest there is some correlation.
Of course, if the result is a chance distribution on both sides, then all we'd prove is that this particular experiment yields no supporting evidence of past lives. You can't *disprove* past lives, or any other hypothesis, you can only show it's weakness in predicting outcomes.
Unfortunately, proponents of "woo" are remarkably stubborn. Their theories consistently fail to predict outcomes in line with observation, yet because it cannot be logically disproved, they assert equal status with theories that do align with observation.