Jon,
Too bad the tray is back on -- the most secure way to apply snaps in that situation is to use the ones that have a machine screw thread (nut behind the tray edge). It seems like the tapping screw ones will eventually strip out no matter what when driven into a relatively think substrate - like the tray or coming. Ditto for the screws that hold the panel to the tray if they strip out.
I have several that pulled out of the (out)side of the coming that were from the dodger. I had no way to get to the backside to use the machine-screw snaps, so I had to devise other means.
If you have thin material (like the tray, etc,) you can soak a piece of foam (foam ear plug works) in epoxy resin, stick it behind the tray edge, and voila' a new, thick substrate to screw into.
If you can't get to the back side, you can drill as large a hole as possible that the fitting will just cover, stick an epoxy-soaked earplug (squeezed out dry) thru the hole -- leaving about a 1/4 of it outside. Just when the epoxy kicks, slice it flush outside with a razor blade. The inside expands and voila', forms a foam/epoxy "wall anchor" to screw into.
Another trick where the substrate is a void (like the coming) that you cant get behind -- fill it with expanding foam (carefully!) When cured, rout out some of the foam (dremel bit, or wire, or bent nail through the hole w/ a drill) and fill the new void in the foam with thickened epoxy. Voila' a new "strong point."
kk