I suspect the Stock Lens Matching tool does not test the stock lenses twice (both direct and flipped). Can you confirm this?
I'm testing on a finite-conjugates system with two cemented doublets and it looks like the best result is not following the symmetry principle. Indeed, when I flip the first doublet I can reach far better results.
Stock Lens Matching tool - Lens flip side
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I think the key point is, if there are two identical and symmetrical lenses set (or doublet, triboulet) in the system,
when replacing them, make sure that they are also identical and symmetrical lens combinations.
In this condition, you can only replace the left one to stock lens, and just copy and flip for the right one.
Maybe it is not easy to examine the system has identical and symmetrical lenses set.
For example, try to find if there are two surface has the same parameters but only radius has opposite sign, then we can say they are identical and symmetrical.
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