It worked. I did some thinning tonight as a test run.
My raised beds are open on the bottom but the tilled soil is 10-12 inches deep and in the past I've had carrots reach that depth and stub off. Plus potting soil made them super easy to pull. Side note: after I had carefully sprinkled my carrots seeds onto my soil, and covered them with a light layer, a raccoon got into the garden one night and felt up all my pots and made mountain ranges out of my smooth soil. I just smoothed it over and they ended up pretty well distributed.