Andrew,
I think that normally you want very new growth to try to get to root. You will have better luck that way. If the limbs are not too big you might want to try grafting on to a root stock of your choice.
I'm out of ideas if they are to big. I don't know if there are any thing to do with them.

Charles

You do not want the new growth. You want to take the hardened growth below the new growth about pencil size diameter with 2-3 leaves. Plant in smaller pot, wet the soil and place in a large clear plastic bag or overturned 2-3 liter bottle with top cut off to make a mini greenhouse. Needs light and warmth to root. If you have the growth hormone then use it. Keep soil moist, do not allow it to dry out. In about 5-6 weeks if leaves still green then your okay, no peeking at the roots. Do not repot for first year. I have 6 moro blood oranges and 2 meyer lemons going right now. They are on their 3rd week and looking nice and green. Good luck.