Is the area above them accessible? An attic perhaps? The ducts are metal? The ceiling is plaster or ? .

This post was edited by bus_driver on Sat, Nov 30, 13 at 21:39

The area above is not accessible, it's in basement ceiling under the first floor. The duct is metal. The basement ceiling appears to be plaster on drywall.

another pic

So these are under conditioned space? If so, the sealing of the duct to the edges of the ceiling material is much less important than if the space above was attic.
Several ways to solve your problem. One would be to get sheet metal angles bent and riveted to the duct to provide a flange for attaching the register. The angle would be as long as the duct is wide- 4" perhaps?. The leg of the angle in the duct would be placed vertically and pop riveted to the duct.The other leg would project out from the duct and lie flat against the ceiling. Make some from heavy paper to be sure you understand the concept. Legs about 1 1/2" or similar?
Use heavier metal than that of the duct, at least 20 gauge and 18 would be better. The duct is probably 26 or 28 gauge.
On a personal note, the first clowns working on my house about 10 years ago tried to do the same crappy work. My late father was a sheetmetal worker in the shipyards before WWII and then was on a repair ship while in the Navy. I have his tools but not all of his skills. This is an easy fix and not doing it properly at first is not excusable. If you find that this works for you, why not do all of them now to save a problem later on.
Let us know how it works out.

angle the screw to screw into the supply box.
and seal the gaps between the supply
box & the plaster before installing new grills.

best of luck.

Hmm, I have some contractors coming to do various jobs. I'll see if they can do it. Have no riveting skills, lol!