I'm not an expert at this, but I have raised two houses, both for very similar purposes as your project. One was lifted with jacks, the other with a crane. I've also been involved in the transportation end of a couple moves performed by professional house movers. Also, I think this is the first time I've ever said "watch TV" for a solution, but in this case there have been some very good shows on house moving by experts. There have been episodes of "Modern Marvels" showing this, as well as "Heavy Haulers." With a little searching on Hulu or Netflix, you can probably find the episodes. For and example of how NOT to do it, the very latest episode of "Ice Road Truckers" showed a house move of a building very similar to the one in your drawing being lifted and moved across the city in Fairbanks, AK. They threw a couple beams under the house, got forks from a forklift under them, lifted the house with the forklift and backed a truck under - very dicey.
One thing typical of other structure lifts that is different than yours is that typically all the shoring beams run in the same direction perpendicular to the floor joists. Seems to me that this is simpler and there are just less ways for things to go wrong. One potential problem that I see with the present scheme, is that it possible to jack the longer beams higher than the short ones and lift the long beams off the short beams - not good. This probably wouldn't happen if you have the kind of hydraulic manifold system like Cooper mentioned above, but since both you and the contractor are trying to figure this out, I'm assuming you probably don't have that kind of equipment and will be forced to manually operate each individual jack. I would consider placing two additional long shoring beams placed just either side of the central existing beam. Then, relocate the short shoring beams perpendicular to and underneath the four lengthwise beams, and place all jack locations under the short beams. I would put 4 jack locations under each of the two short shoring beams in locations so that any two jacks located on opposite sides of the building central beam are capable of carrying the load of that beam even if the other two jacks were not there at all - 8 jack locations in all.
If you don't have the manifold type hydraulic jack system, use screw jacks instead of hydraulic jacks. They have plenty of lifting capacity and allow very precise control so that you can raise them in very small equal increments, allowing you to raise them one at a time (applying common sense to the order) while moving the structure out of level only a tiny amount.
I wouldn't bother with the temporary bracing. Instead, design the cribbing to provide safety. I would think that if the cribbing is designed and placed in like manner as would be done to support a crane, that should be more than a sufficient safety factor and that house won't be going anywhere during the construction unless there is a hurricane, tornado, major earthquake, etc. Any of those occurrences would probably treat the temporary bracing as so many toothpicks anyway. Crane cribbing must be designed so that the entire weight of the crane and load can by supported by any one of the outrigger supports. By the way, the cribbing as presently drawn would not be considered adequate for a crane. Assuming the cribbing has adequate ground bearing area for the load, the timbers must still be placed side by side the entire width of the cribbing in both directions. In other words, fill in the empty space between the 8 x 8's with more 8 by 8's.
