Massive turnips in cover crop

Bit of a noob question- I planted a cover crop mix last fall that included purple top turnips. It was supposed to die off when it got cold but then we had a warm-ish winter and the turnips kept growing and got huge. I had planned to just sort of gently chop all the dead matter into the soil and then layer over with compost for this spring, but that doesn’t seem like it would work for the turnips the way I pictured. Would leaving them in the ground cause problems? Would y’all go through and pull them? I have chickens I can feed them to if I do pull them

I had a similar experience last year with some turnips that overwintered rather unexpectedly. I took an ice chopping tool and chopped them up in place with good success. My chickens would eat turnip greens but were a little shy with the bulb itself. To be fair, I only rough chopped it so the pieces might of been a little to big for them to handle.

Those turnips should be very good eating too. After they are touched by frost they get quite sweet. Maybe put a few in soup too?