Egon is on to something here. The BH can loosen up the roots enough that you can knock a tree like that over with the FEL, or pull it as Gary describes. Don't try this with dead trees or ones with widow-maker branches, though. Are you cutting the tree 10-12 feet up or is that just where you're setting the chain using a ladder or something?
This is just me, but after trying many different methods, including the chain-pulling approaches mentioned here, I've found simply felling the tree and grubbing out the stump with the backhoe is generally the safest approach, even though it may take longer. If you make the felling cut a few feet up, it gives the backhoe more leverage to release the stump.