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A decent ski tech could fix that in a way that would be lasting and still ski just fine with a good base patch. Eventually you would probably pop the patch out but the skis look pretty beat anyway so it would almost certainly make them last long enough.
You get a sheet of base repair material (basically a big piece of what your bases are made of) and cut out a square large enough to cover the damage. Place that on the ski over the damaged bit then trace around it precisely with a scalpel. Take the patch away and keep re-cutting with the scalpel until you hit the core then, with a wide, sharp flat chisel you chisel the square of damaged base off the ski. Clean with prepsol or similar, roughen the surfaces, mix epoxy and apply to core and bottom of patch. Since you traced around it the patch will fit perfectly into the hole, just like a diecut base. Clamp the shit out of it and put it under a heat lamp until the epoxy cures.
Usually the patch sits slightly proud of the base (depending how thick the original base is and how many base grinds you've had) and for a smaller patch I'd say knock it flat with a bastard file (check it with a true bar) then structure with a brass brush but for a patch as big as you'll need I'd just chuck it on a belt.