Is the house on timber or concrete stumps? Whereabouts is the house located?
Cost of packing (levelling) the house can only be done if it's <=50mm out and costs around $1500 or so. Depends on the size of the house and number of stumps. If they're out by >50mm it can't be packed and you'll have to dig out the stump and replace it. I'd suggest steel posts with adjustable heads.
The first thing to do is to get a soil test done. Should range from 350-500 for 2 boreholes, testing and a report. At least you can get a classification of the site's soil reactivity, and borehold log so you can get an idea of how deep you need to go if you restump. If you don't go deep enough you might not acheive enough bearing capacity for your new stump and the problem will still be there.
Once you get the soil test done, try and get a line/water gauge out there and get any idea of how far out each stump is. Packing the house will level it and re-distribute the loads across all the stumps, causing it to start moving again. Getting someone out there to measure the levels will cost you $$.
I got quoted about 450-600 per stump, to remove the old stump and install galvanised steel posts with adjustable heads. Obviously depends on quite a few things like material (type of galvanising - hot dipped?, height of post, if concrete doming or larger footing is required etc).
Sure, if you can pack it, you could try and do it yourself, but restumping is hard work and not something I'd want to DIY. At least if it's an IP it's deductible. I'm getting a soil test done next week myself