If they are already forming storage roots, the thinning is way late. No blame. Sounds like me (grin).

This is the problem. The tricky part is that you need to preserve the many very thin almost invisible roots and root hairs that are attached to the 'carrot'. Those are the things doing the work.

If the plants are far enough apart (several inches apart) that you can dig out and 'transplant' the thinnings without disturbing these all these fine roots, it is not impossible that at least some will take in another row. If they are close together, even thinning them now might rip or damage those feeder roots on the ones you want to save.

If it were me, I would clip to the ground the plants that were not the strongest, rather than 'thinning' them by pulling. Keeps you from cutting/ripping/killing the fine roots on the carrots you want to harvest.

My personal mantra.... "Next year. Ok. I can do this."
(wry grin)