I think you are right. The copper will intensify the warmth of the cherry, especially over time, as the cabinets deepen in tone. Copper likes to be the star and calls a lot of attention to itself, which may limit what other colors work in the space.
I'd go with the tin.

I agree, I think you are right

I would prefer a simple, rich, deep, mellow copper to tin but would be concerned about the light for a kitchen. I don't see a connection with a silvery tin. I think that would stick out more. The ones I have seen are shiny and ornate and take center stage anyway. They usually clash with their surroundings, imo. I think a metal ceiling takes some know how to pull off well, so be careful what you are doing and the overall effect and style you want.

You can google some images, if you haven't already done so.

What is the flooring and color?

Thanks for the feedback. I agree that the unfinished tin does not have anything to tie it into the design at the moment.

Flooring is going to be original (1929) oak, if it has survived the previous renovations. Right now it is under a couple of layers, so I won't know til it is uncovered. The finish on the floor is undetermined, the rest of the house has a natural/golden oak stain.

My SO also suggested painted tin panels, keeping the architectural look but going with a more neutral finish (white/off-white/crackled/etc).