Can you (would you) describe the timbers, as to species and as to what kind of damage they cannot sustain? I take it you cannot slide, roll, or dump them, meaning they will be exposed inside a building, such as a timber frame.
I would opt for the sling arrangement, and hook them as close to the front of the tractor as possible (not wanting to damage the hood or grill) to get maximum lift from your FEL.
I took on a pallet of shingles last fall that I could reach and lift with my 430 FEL forks on the Deere 4300. As I backed up, and the pallet came past the edge of the truck, the rear wheels began to come up as the front wheels turned a bit. Fortunately, I could quickly lower the FEL to not destroy the shingles, but they were a bit disarrayed on the pallet when finally resting on the ground (the agreement was that they would be loaded 1000 # to the pallet, but instead came almost 2000#). I thought I was okay as long as I managed to lift them clear of the truck, but didn't take into consideration the wheels turning and changing the balance point (fulcrum) of the 'system'.
Good luck with the timbers.