They are Nola Mini's. Yes, one screw was already stripped out. It will back out but it won't tighten. I guess I can contact Carl Marchisotto at Nola. I was thinking a slightly larger screw but I know nothing of speaker cabinets.
No, don't go installing larger scews - that only leads to larger screwdrivers which leads to larger hammers and then, eventually, to very large wrenches and then to humongous winches with really big motors. You can't hear the music over the noise of those motors.
Carefully, run a drop of yellow wood glue or Elmer's glue down the screw hole. No Gorrilla Glue or anything other than glue meant for wood. Be careful not to get glue between the frame of the driver and the bafffle of the speaker. Place the tip of a toothpick down into the screw hole and allow the glue to set up. Break off the remaining portion of the toothpick at the driver basket after the glue has hardened and reset the screw. If the screw still won't tighten, redo the procedure with another toothpick.
MDF does not accept screws well. It's very easy to strip the screwhole when you are attaching anything to MDF.
Make certain though you are not overtightening the screws on the driver. While MDF strips out easily, it's not always best to have driver screws extremely tight. Many drivers have a particular torque range where they behave their best. With some drivers having a screw just tight enough to hold the driver in place is the best thing for sound quality. Try tightening the screws on each driver just to the point where they are snug without air leaks . Listen to some music and then back the screw off about 1/2 turn. You might find you prefer the sound of the speakers without super tight screws.
While you have the screwdriver out though, check the tightness of the binding post cup on the rear of the speaker. These should be tightened sufficiently that no air escapes from around the cup when playing music with heavy bass content.
If you can remove the driver without destroying the gasket, the job is a bit easier. But not much to worrry about either way. Even a small bit of glue under the driver's frame won't be a disaster though it will probably mean you will have to tear the gasket if you ever need to remove the driver.