Hi John, I haven't seen this approach before. I have some experience as a project manager that had houses raised for foundation repair or crawl space clearance though. If the beam sits in a pocket just jack it up and shim at the pocket, lower the Jack, shim under Jack etc. the trickiest part is stabilizing the jack and whatever it is sitting on.
Some more info is required to give a better opinion.
Is this a ridge beam?
Are there rafters attached to the beam?
Is there sufficient support for the jack's point load?
Is it a vaulted ceiling?
I have used dunnage to support beams. Jack up, support beam with dunnage, lower the Jack, Raise jack higher up...etc till beam is at the desired height.
Dunnage can be almost anything like stacked pallets for instance. If jacking off a lower floor, dunnage sitting on floor will help distribute the beam load of and the jack, though I would keep the beam stacks and Jack stacks independent and perpendicular to the floor joists unless your jacking up off concrete. If using pallets, stack alternately on your way up. Most of the work I did was for clients and safety always came first.
It could very well be that I am over cautious and the system you posted may work very well. I just don't have past experience with it.