My theory is that if you place a thin glass (an actual aftermarket glass, or a tempered glass) and use a liquid adhesive to stick the thin glass (though the glass should already come with adhesive) the scratches wouldnt be visible anymore. It should work by letting the glue fill the gap and letting the glass keep the gap filled flat with the glue so it keeps the scratches "invisible".
Of course I realize that if your intention is to keep the screen bare, then this answer will not help in anyway. It's just one option to consider. Pls let me know what happens if you decide to try