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?

Well it's sort of a good problem to have! The only downside I can see of leaving them in the ground is that they will go to seed - early flowering so good for pollinators and predatory insects. Also not so good if you were intending to plant something else there. If you pull them and leave them on the surface they may try and carry on growing for a bit. The smaller ones will probably give up, but the bigger ones may well be quite persistent. I would do as Timothy and M Lijn suggest and use what you can - bonus early season crop! I'd be tempted to leave or relocate some for seed saving anyhow.
If the chickens aren't keen, you could try hanging them up for them to peck at rather than leaving them on the ground or in a bowl.