I'm not saying you won't find Micarta that thick, but I've never seen it that thick before. You might try Westinghouse web sites. I think they are the ones that developed it for insulation with high votage electical equipment.
As for buying thiner sizes, Binghams, or a good knifemakers supply house would be your best bet.
The glue to use would be Smooth-on, just make sure you sand off ALL the shin on the surfaces to be glued...matter of fact, after sanding, you should probably scar the surface with a hack saw blade, this would give you small groves for the glue to get down into. That would work for sure.
Hope you find what your looking for.