If it was me, and I knew the desk probably wasn't long for the world anyway, I would probably just patch it - get a piece of wood just big enough to cover the hole and distribute the weight, glue/ nail that in place over the hole, and then screw into the patch. You could do it on either the top or bottom of the desk, depending on where you'd least like to have the patch in the way.

Of the things you listed, i would try epoxy putty as the strongest filler. Apparently they even sell it as "Wood filler" now for just this function. Although iirc the last time I used it, it is a little tricky to use, but maybe it's gotten better in the last five years.