Has anyone tried tying lead fishing weights, rocks, etc. to such plants and
holding them underwater for about 24 hours while the fish feast on the aphids?
I haven't, and at the moment don't have any floating plants with aphids, but
apparently some of the folks on the APL do.
I don't have a pond or anything, but your might try to get a hold of some ladybugs. They love aphids. BTW, how do aquatic plants out in the middle of the water get aphids?