house sitting on wooden beams?
Jacking up a house to install a new foundation is an advanced DIY project, with the potential to get you killed if not done properly. I am surprised that a professional foundation repair company would tell you to go do it yourself, I mean isn't that their business? Are they so busy they haven't got time for your project?
Before you undertake such a project, you need to do a lot of reading about temporary support, permanent support, and safety procedures. Certain types of jacks are totally unsuitable for the project (read car bottle jacks) because they tend to bleed out when you need them the most. You also should have a chat with your local building inspector, you may not need a permit to do this, but they may have some helpful ideas. It would also be a good idea to visit someone who has actually done this before you consider doing it yourself. Kind of like repairing a car transmission, not for everyone.