CA a piece of dowel in the hole. When the CA is dry sand any dowel sticking up even with the servo tray, then drill a 1/16" hole for the screw. Put the screw in, then take it out and put a drop of thin CA in the screw hole. When the CA dries install your servo. The CA will harden the threads made by the screw.

A tip for you:

RTL Fastners has socket head servo screws with a built in washer. They use a 5/64" ball driver. Much easier to install than the philips head or slot head screws.