Hi Blade Butcher, welcome to Outdoorking. Very sad about those screws being stainless, chances are not even Deejay's trick of dragging a magnet around the lawn before mowing, would have worked. (I'm guessing they were austenitic stainless and therefore non-magnetic - all my stainless screws, washers and nuts are.)
You can grind the reel blades down pretty much until they nearly reach the lateral separators before giving up, but what we really need is a picture or two showing the mower for model identification, the reel to assess how much meat is left, and the chains and sprockets just to contemplate how close you are to having problems in that area as well. Then Deejay can get into discussion with you about the overall health of the beast and how to make it nicer.