Cheapest way to level large concrete floor without losing height
There isn't much you can realistically do that will make those slabs even: either one has to come up, or one has to go down. I don't know what options are available for mudjacking a slab with a house on top, but if you could even find someone that can do it, I'd imagine both the cost and risks would be.... a lot.
depending on how big the gap is, you might be able to level it with epoxy. There are self-leveling coatings designed to fill gaps and cracks. You could also try using vinyl floor tiles to make the transition more gradual.
Probably the easiest (and cheapest) thing to do would be to get a big diamond grinding wheel and bevel down the lip. It won't make the slabs even, but at least you won't trip over it anymore.