I want to replace some aging flood light fixtures on the outside of my
home. I bought some motion-sensing flood light fixtures and went to
swap them out, but I discovered that the electrical boxes are too
small. The mounting screws in the boxes are spaced roughly 2-3/4"
apart, whereas the screw holes in the cover plate for the new fixtures
are ~3-1/2" apart. They are also oriented differently: the two holes
in the box are in the lower left and upper right, whereas the holes in
the fixture are in the lower right and upper left.

What are my options for attachiing these things? Is there some sort of
adapter ring that will allow the new fixtures to attach to the old
boxes? Is there a better solution?

Your kind advice is most appreciated.