I normally set the verts to be constrained to edge, and then move them manually till they sit on the surface. Then I target weld the other side to it. It's almost 99.9999999% accurate, depending on how well you eyeball.
this is pie, go to your top view, and select 2 opposite each other and scale, yup, just like you did before, but this time before scaling, do a shift -x or manualy turn on constrain to edges, scale the verts together and poof magicaly delicious