Thanks again Dave. I think the shims I have are .010" down to .002" but I can easily get some stuff at the Home Depot. Actually, tin cans make pretty could shim material. I did some googling and apparently any attempts to manufacture an 870 shim product has flopped, but it should be even simple enough that I can knock something together.
I wouldn't be surprised if the range's patterning board is set up at 16 yards, as it is just past the last trap house and the distance looked to be about the same as the front of the house to the front line.
Meanwhile I keep drilling in the mirror and think I may have gotten the proper mount. The pattern board may just confirm things.