Chris and JCS: I think your math on ISO increase is either coming from remembrance of the inverse square principle or from working with "speed booster" adapters where we almost literally squeeze the image circle down and thereby increase its intensity. But that's not what's happening here, we're merely sampling a larger area of the image circle--the ISO doesn't change.
Imagine a hypothetical lens with a 10" large image circle. You put up an 8x10 sensor (of a fixed ISO, let's say) to capture it and you get X for an appropriate exposure. Now tear that sensor in half twice, and it's still the same exposure (X), but you're only sampling 1/4 of the first image. Now tear it to a full-frame size, s-35, and s-16 and you would continually get a smaller and smaller portion of that original angle of view (fewer degrees, rendering the same lens more telephoto) but still the same exposure.
In other words the over-exposed image looks over exposed because it's over-exposed. Crop-factor math only matters with respect to trying to maintain the same DOF in the smaller sensor (on the "wider" lens) by opening to a wider aperture--in which case you would need that much less ISO in order to keep exposure "X" the same. X stays the same
Perhaps you missed this:
If you don't care about matching DOF and FOV, set the C200 to F5.6 in this example (same as the FF set up: focal length and crop factor won't affect exposure. Prove it to yourself with a zoom lens with constant F-stop (ideally T-stop) as well as enabling, disabling the C500's II S35 and S16 crop settings).
I posted equivalence math and examples in the event the OP wanted to match cameras in DOF + FOV + exposure.
This info comes from doing the actual tests and verifying that the math is correct (including ISO):
[Shot with the Sony A7S and Canon lens (no SpeedBooster)]
Shot 1 (FF):
Shot 2 (cropped):
Are these shots nearly identical? From https://brightland.com/w/the-full-frame-look-is-a-myth-heres-how-to-prove-it-for-yourself/
When I first posted these results 5 years ago, many folks didn't want to believe the Full Frame Look was a myth- perhaps that's still the case with the downvote.
An interactive example: https://dofsimulator.net/ (for DOF & FOV)