If you were to cut the roots, how many are we talking about. Out of the whole tree's critical root zone, if you were to cut these roots, what would be the percentage? 1-5, 5-10%.
In my experience, cutting roots that size is not a big deal and should not adversely affect the tree. I worked on a project at the US Capital where they were installing bollards around the perimeter for security. No trees could be cut down so we had to air spade through the root mass so they could install the bollard. We cut roots much larger in size and did not harm the trees. I know what you are trying to do because I've tried it myself. Most engineers don't like things growing through their footings.