If I read this right the right rear is 4 inches lower than the left front. If the floor was built crooked, and you now level it, wont the walls, which were presumably built vertical, now be crooked? There gotta be a hunnerd other little things too, like your kitchen cabinet doors slamming shut, windows now crooked, What about plumbing? I dont know the layout, but it seems if you tilt, or untilt, the back of house that much, its gotta affect the slopes of plumbing drains. It also sounds like you a lifting different amount in different areas of the house. That means the house will be flexing. Things are gonna crack. Even if dont crack on day one, down the road the house will resettle.

I looked into raising my house, to increase the basement headroom. I “interviewed” all the listed house movers in my area, three came to look at it. No cracking was important to me, as we had recently done a lot of remodeling. All said there is no way it wont crack.

I think you should show you house to a house mover, just for the opinion.