The paperstone base is 1-1/4" thick and the mounting screws are 1-1/2" long overall (1-3/8" thread length-excludes the flat, countersink screw head). If I add the washer (metal/rubber) as I originally asked about, there is not enough male screw thread protruding from the top of the paperstone base to be able to engage the sharpener base female thread.
Surely I am doing something incorrectly.
Sorry to be such a bother, but...
If you push the screws through the washers, then the base and they stick out enough to get a little thread engagement with the sharpener base, then that should be enough because the washers will compress quite a bit and then you'll have plenty of thread engagement. Please let me know if that works. Otherwise, we might have sent the wrong screws.