I did some googling. I found some women cycling forum people talking about using those felt furniture pads cut in shape as shims. Those pads have adhesive on one side. The felt side doesn't compress that much since they go under the furniture. Others suggest to use cabinet rubber bumpers. I think the tricky part is to get the right thickness because all those solutions are not adjustable.

I too wish there're longer screws available. That way the reach could be dialed in exactly where it needs to be.