Always test fit replacement parts before remounting the radio..
If those screws don't go all in by hand before you mount that back up, this is the stuff that happens.
When I fabricated my own mount, I dug some trim/panel screws out of the parts bin that had the same pitch and some extra length. Take the OE to the hardware store if you must and find a (longer) mate.
Those inserts in plastic are not meant to support a lot of torque OR weight. They're there to provide shear support for the radio bezel. I almost think they should provide a thin U shape bracket with nut to put on the underside of the radio mount. Or perhaps just a flat piece with a new nut to spread the load. As it is, the tiny flange of that nut is taking a large part of the load of all those levers you put above. I dunno, maybe it's more of a side load than a tension load that I'm thinking.
That said, I did find after running a flat plate for a while that if you don't fill that void below with washers or a plug or standoff of some sort, where the screw cup is, it will eventually warp and deform both the tray and supporting screw mount after time in the sun.
When I redid my setup and installed a Rubigrid, I designed and printed a 3D base to fill that void and angle the Rubigrid up enough that I didn't have to file down the corner.
