"Do these American storage pots look anything like it?"
I wish!!!!
I think you might be right that mine could be older than the Celtic pieces. Mine has a lid and a holder(? not sure what you call it) for the lid to sit on. The Celtic ones are vases and not lidded. The unglazed interior is a lighter, more yellowy colour than the unglazed areas that can be seen on the base, which are darker. The same also for un glazed areas around the rim and on the bit that the lid sits on.
I might just take it along to David Ley's free evaluation day on Monday. They are auctioneers down in Penzance and flog a lot of ceramics amongst other things. That's if I can find a wheelbarrow or a forklift truck!!! I might also take the "Troika(ish)" one too.
Lots to think about. May be worth me contacting that American link (and the local link that you gave) with some pics. to see what they think also.