> I like the idea of the stainless steel mesh glued under the drain holes.

Agreed!

Several years ago I glued some of those mesh hose washers used in the
water lines of washing machines.  They seem perfect--glued on the bottom
with the bulge coming up in the drain hole. They turned out not to work
very well--the mesh size is too small, so they clog up with dust and
little crud.  I think a medium mesh on the bottom would work better.  I
got some aluminum [or aluminium] screen, but procrastinate in removing
the luggage carrier since it doesn't rain any more....

Richard