In my experience 'defacing' the Thomas engines, those face screw heads are easily stripped because most modifiers do not have a short enough, right size head, screwdriver to get into the narrow, short, engine shell to remove the screw straight on. So most use a normal sized (too long) of screwdriver which doesn't allow the Phillips head wings to fit correctly because the driver is on an angle. Works most of the time but if the screw is too tight the head will strip out as shown.
If you have a Rotary Tool with a thin cut-off wheel/disc you could try slicing a groove in the head and then use a slotted screwdriver. I would also suggest trying to warm up the plastic where the screw is, with a Hair Dryer but do not heat it so much that the plastic gets soft or damage any stickers/decals. You may want to at least try the warm up method first and use the screwgrab/rubberband methods you tried before but be careful with the heat.
If you have a Rotary Tool with a thin cut-off wheel/disc you could try slicing a groove in the head and then use a slotted screwdriver. I would also suggest trying to warm up the plastic where the screw is, with a Hair Dryer but do not heat it so much that the plastic gets soft or damage any stickers/decals. You may want to at least try the warm up method first and use the screwgrab/rubberband methods you tried before but be careful with the heat.