I've done a few of these and a hydralic jack worked fine with some buildings. Usually with a solid post back-up (while working on it), size depending on the barn in question. Some jobs you gotta have cribbing for the added stability. Screws jacks are supposed to be great for lower buildings raised by hydralics. I use hydralics almost exclusivly , but I would warn rookies about letting them down ( and going up) they can be deadly.
Great joinery! My clients usually don't aprieciate that level of joinery (the're cheap) so we usually use a 2' lap w/ 3 bolts w/ washers.