I would be very relucant to cut many of the roots. You would regret it severely if you lost a big shade tree and cutting through roots creates such a risk. Nor should you cover with soil, with also can be very risky. I know that limits your options, but you would never want to lose such a tree. In any case, if you were to put pavers over roots, you'd soon find they roots would be creating all sorts of havoc. Perhaps, instead of a patio, you could install a low deck supported by footings and beams, so it's not laying on the ground, but barely above it. Or you might think about a gravel patio instead of pavers. You could spread several inches of gravel and, unlike soil, it wouldn't suffocate the roots.