The typical J-head machine with a long table is about 2050 pounds so the engine hoist might just do it. It would be a straight vertical lift.
You can use an eye bolt in the tapped hole in the ram - you may have to adjust the position of the ram and the saddle/table to balance it out. You can use lengths of pipe to roll it into position Egyptian pyramid style, then use pry bars and wood blocks to get it off the pipes. It's not all that hard - just take your time. Keep the knee low and the saddle back. You can tilt the head all the way forward to help lower the center of gravity also - just clean the gear on the knuckle before you crank on it.
Good luck - keep us posted!