Do you find that matte finish dials are the most risky to attempt it? I did have minor luck with glossy/clear coated dials in gently removing surface gunk but I would be very scared trying it on that speedmaster dial you saved. Experience would be key I am sure.
Well the first thing I do when cleaning a dial is to have a lengthy and very frank conversation with my client. I want them to understand the risks and possible damage that might happen, and usually the request to have me clean the dial stops there. In this case, the customer was accepting of the risks, and my confidence in cleaning this dial was much higher than it would be for a lacquered dial. In addition, the round portion of the small seconds hand would cover damage in the unlikely event that it happened in this case, so there are a lot of factors that go into making this decision to clean.
In my own experience, if the dial is matte or glossy hasn't really made a huge difference. For example the old silver dials that you find say on ladies watches from the 20's, those have dials that are matte but can be cleaned quite aggressively, and they come up quite well.
One risk with matte dials is that you can "flatten" the matte surface with even light pressure sometimes, and it will create a small spot on the dial. But by the same token some high gloss dials can be scratched really easily.
I clean dials using these sticks...
They don't leave any residue behind (like Rodico and similar products can) and they are tacky enough to lift dirt, but usually don't lift lacquer unless it's already so loose it's falling off. This is a part of what I used to clean that Speedmaster dial, but the rust stains would not just lift off. I used a piece of peg wood, and cut the end to look like a slot screwdriver blade, but I cut it very thin at the end. This makes the end of the peg wood sort of "feathery" with the wood fibers, and I used that to very gently sweep over the rusted area, and it slowly came off the dial with zero damage. The sticks were used to pick up the material once it was loose.
Delicate work, but it can be done.