Looks like that shim will work, but I would measure the parts if I were doing that. 16 gauge sheet steel might also work.

I have two Klein bikes, but neither has the Mission Control stems. When I replaced the BB bearings on the 1983 Performance frame, I couldn't find anyone who had the Klein BB service tool, so I had to improvise. It's great that you could find the appropriate tool.

I have Deda Zero100 handlebars on my 2006 Q-Pro. They work well for me, so I think you'll like the RHM02 handlebars.

Keep us updated on the project.