I looked through my current collection and I don't seem to have a great deal of detail on heavy lift.
My experience with this is a bit limited. I did work with a house moving company to lift my first house (a turn of the century Victorian)....but that was a full 18" lift and the company had all the hydralic equipment you could imagine.
As a young lad, I worked with my dad (a GC) on a couple of individual house lifts, using 5 to 40 ton screw jacks. The value of using screw jacks is that you can load your weight bearing members GRADUALLY, and keep the load on the jacks for weeks without hurting anything....something you can't do on hydralics. But keep in mind that when wood goes into tension (sags), it will take quite some time to put it back to level.....if it can be done at all. So your idea of going to steel may be a good one.....the only question is will your local building code allow it. This will be a very important issue; if your house burns and it is found afterwards that the reason for the structural failure during the fire was the use of steel which was installed without a permit, the insurance company may not have to pay :-(