Can someone help with how to get the plate flush with the table?
I've had leveling screws strip out in press-board before on my router table top and I drilled a 3/8" hole where the screw was and inserted a oak dowel with glue. Much better than screws in press board..This is a technique I learned many many years ago for repairing stripped out door hinge screws..
Try using 8x32 thread brass inserts. You can probably use the same holes in the MDF that have stripped out, to install the inserts. Rockler sells small packs of all sizes. The ones I use have slots on top, so that a flat screwdriver can be used for a quick install. The insert allows use of any head-choice with a machine screw, as long as the thread is the same as the insert. I use screw heads that allow use of an allen wrench for quick adjustment. The weight of the router will keep the screws from moving. To smoothly install the inserts, I rub a paraffin stick across the outside thread of each insert.