Why aren't you worried that they might freeze? Wouldn't you have frost by Oct if not Sept and ground freezing a month or so after that?
I think if you cut off the tops and force the carrots to regrow their tops, they will take what they need from the roots, deteriorating their quality.
Carrots are said to get sweeter after first couple of frosts because like most plants, they will convert stored starch in the roots into sugar as natural anti-freeze. In Japan where regional gourmet branding is the popular agri-marketing practice, they sell post frost carrots harvested in northern, snowbound prefectures as "Snow Carrots" -- a gourmet seasonal item only available for limited time in limited volume.
Are you going to miss the harvesting window? Would it be better to harvest and store in root cellar or something? Or maybe force the carrots to go dormant by heavy mulching and preventing the tops from re-growing.
...I can only speculate because here, if left too long, carrots are riddled with tunnels by wireworms as well as carrot fly maggots. I usually let those overwinter and bloom next year. Sometimes, burrowing animals -- chipmunks, field mice, etc.-- find them and they don't come back.