(guess that teegee knows this :-)
I appreciate your confidence in me but this sounds a bit like having your cake & eating it. Am I correct? ;)
I have cut off all but a couple of the heads I am left with these huge cabbage-y plants.
I need a crystal ball answer this one but here goes;
Firstly it will depend a lot upon the weather if you get any more spears of broccoli, you certainly won't get any more heads.
So next thing is; if you want to prepare your ground for this seasons crops then lift them, if you want to leave the preparation till later then leave the broccoli plants in and you might get a few more spears.
My vote would be to 'prepare for this seasons crops.
I also have some calabrese broccoli that still sprouts some small florets but nowt much to speak of.
The same as mentioned above will apply here also.
I also have some roundhead smooth cabbages: some have gone a little mouldy but we are slowly eating through them. I have some regrowth on some of the stems but when do I actually dig them up?
Initially do what preparation you can without moving them, then as you are ready to prepare the area they are in, lift them if they are in the way of new produce, if not leave them growing until last gasp.
And how can I compost these huge cabbage stems?
Yes providing the plants are not diseased e.g suffering from club root.
I hope that answers your question.
Just a point for the future; You will most likely faced with this quandary every year so fit these late plants into your rotation and autumn digging plan.
I generally plan to follow these late plants with salad and fast growing crops so this allows me to prepare the remainder of my plot/s and leave my winter greens to mature.
Then in late spring / early summer I dig up what is left and sow & transplant as necessary.
So after all that it comes down to............planning!!