Also " layers of shims" is a terrible way to build a shim. BTDT.
If I was doing custom work like you are I would do a single milled shim per the specific application.
But as for stacking shims,actually not true it not done or advisable. I don't know if they still do it but back in the 80s they still used multiple shims on equipment. The ability to mass produce to a tolerance fine enough for one was not there yet. So you would put in one thicker one (for this discussion call it .010, thick being relative) and then have stacks of .001 to .009. Had a final drive on a BMW cycle that was just that.
Put in the thin shim to get the set and you were good to go.
Now you may think I am trying to smoke you, lo many years ago I also was directed to restore an old 10 hp Kellogg American compressor. On taking it apart I found the tapered roller bearings chewed up. Ungh.
Got the internals check and replaced parts as needed and putting back together and scratcfhing my head on finding 7 end cover gaskets. ???????? Ok, we only need one, or so I thought.
In it went and tightened down and even with a big flywheel to grasp, its locked up. Hmm, ok, back to bearing and setting end play and the lights begin to come on. They are setting the end play with a squishable gasket? No, no, no.
So, add another gasket, still locked up. Ok, add two more, still locked up. Add the rest, still locked up. Vern, I am beginning to see what the problem is. They just threw it together and the 10 hp motor started it and ground the bearings into compliance.
So into the OLD gaskets which I now realized were 7 squished together.
I added most of those before I had a free wheeling compressor and then I left it for a few days and checked again to be sure it still was free. Not only squishable, you now have how many leaks surfaces?
So yea, staking shims is not the crime that was. Clearly its not ideal, but it works and depending on the degree of precision invovled, really not an issue.
Its also what they do on prevision alighement work. You are never going to have the exact right shim. You pick the one that gets you the most and then as few as possible sub shiming.
It would be interesting to check an origianl that was fired little and see how badly off they were. I will bet my stacked shims were a miner crime against humantify in contrast (grin)