I think I'd try a putty knife with a V notch ground into the end of
it. A long V, with sides ground from very acute at the open end to
almost vertical at the base of the V. Use it under the tin, and with
a pushing action only - no prying. If you can get it in to the bottom
of the notch, the nail will have broken loose a bit - and you can then
push a thin prybar under the knife and use that to pry the knife, tin
and nail out. Or use a second V notch knife to lift the nail even
further before you try a prybar. This will avoid what in my
experience is the most common problem - tearing the tin at the rim of
the nail head before you can get anything under it. And it won't hurt
the show surface of the tin at all.

So a putty knife wouldn't be long enough working under the tin? Check
McMaster or other sources and you'll find many different similar
knives, spatulas and scrapers, but much longer and stronger.
Printer's ink knives come to mind.

Just my thoughts, though.

John Martin