Heres what I did. My stacks were about 4 ft high max. First I would lay down a sheet of 3/4" plywood, then take my engine puller out and set it on the plywood. The plywood will give the wheels somthing to roll on. The puller will lift 1000 lbs so I by myself had no problem lifting the wood with a strap under the timber. I would then pull the puller back on its wheels until it cleared the stack. Then let it down onto my my cart. I paid around $150 for the puller and it was worth every cent. If I was to it over I would weld maybe 6" rubber wheels to the puller as the plywood used for the pullers 3" wheels would get a bit muddy at times.
Good luck, you can do it, I moved and cut all my timbers for a 7 bent home by myself and only went through 1 bottle of aspirin for those "oh my achin back mornings"