You may want to start using a dice tower. Basically a wooden, plaster, or cardstock tower that you drop dice into the top of, they rattle their way to the bottom, and come out into a tray at the bottom.
The first one I saw was on
this site using the Hirst Molds, since then I have made some from cardstock for friends (I don't use them myself, since I walk to the game with my gaming stuff in my back pack), and have seen some made out of Lego Blocks (the world's best toy!). But Becker's remains the most impressive that I have seen.

And the dice hit the bells making a pleasant tinkling noise!
World Works Games makes a rather simpler one for printing out, cutting out, and putting together.The ones I made from cardstock use pieces of another World Works building, form Castle Works Classic. The animation that is used to advertise it is... campy.
The main point is that it gives an excuse to have the players roll in a single, easily visible, location. And since you have
all the players doing it then the cheater cannot complain.
The Auld Grump, and yes, do get him to go over his 'math' when you distrust his numbers.