I don't know of a way to invert an arc. But maybe you'll be ok by drawing the new arc before deleting the old one, then use the relatively new "Replace Entity" tool to replace the old arc with the new one. This should update all references so you wont have the ID mismatch problem.
Fix the arc center and drag the arc endpoints around and eventually the arc flips to satisfy the geometry.
More hassle than recreating anew, but I guess it is what it is.
Jamil, that could be a plan B ...
Kevin, would you please explain how to do that? I tried dragging arc endpoints in every way I could think of, it didn't flip...