Here is how I would remove it.
Place the tray in a vise in a drill press, this is not a job to be done by hand. I can pretty much promise you if you try this with a hand drill you will do more harm than good...been there done that.
Using a starter drill, start a hole in the exact center of the screw head. It is important to use a starter drill, they are much stiffer than a standard drill and will not deflect like a standard drill WILL. The starter drill will clean out the damaged screwdriver slots, a standard drill will most likely start an off center hole or break.
Drill the hole completely through with a drill that is about 1/2 the diameter of the screw.
Next using a drill about 1/2 the diameter of the screw head, drill down just deep enough to remove the head, this will separate the tray parts. At this point I would heating the tray, boiling water is a good choice since it will not likely damage the finish. With a good set of pliers, grip the remaining screw and try to move it, both in and out. Most likely it will start to turn at which point you can remove it.
If it still will not move, reinstall it in the vise and drill out the screw with a drill about 2/3s to 3/4s of the diameter of the screw. You may have to come in from the back side if you crushed the screw....I would actually recommend you drill from the opposite side. Drill just enough to get almost through the tray, leaving the part of the screw you are grabbing the same thickness. Apply more heat and grab the screw with pliers again, working the screw in and out to see if it comes free. It's likely you will crush the screw at this point, no big deal.
If all that fails, return the tray to the vise, drill out the hole to the correct drill size for the screw and use a taper tap of the correct size to clean out the threads. Be very careful when starting the tap since the objective is to restart it in the original threads, not cutting new ones but rather cleaning out the old ones. A good soak in PB Blaster at this point helps loosen the threads. There are 2 sizes of drills for each tap, one size for steel (larger) and a smaller one for softer metals like aluminum. I would use the smaller size since that is most likely what was used. While you are at it, I would run the tap coated in PBB through the other hole to clean out any corrosion.
Once you have the threads cleaned, coat the screws in silicone grease before installing them. This helps keep out water and helps prevent more corrosion from forming.