Well, let's leave for a moment the discussion if this is a relac or not, but personally, as much as I love Martin saxophones--and I have 2 among my gigging set of horns--I wouldn't pay 12K for one. If the seller was to get that kind of coin, it might--and I stress might, sell to a war history buff.
I haven't check the prices for Pearl Harbour memorabilia like you have Pete, so I'll take your word on that it's pricey. I have no doubt it is, but for this kind of one-off stuff, I think you pretty much set your own price and see what the market will bear. I know of a couple of sax-playing, war historians, so this might appeal to them. The question is would someone of their ilk pony up over $10,000 for a horn that its particular history notwithstanding, might be worth a couple of grand tops? (And that's if freshly overhauled by a primo tech with a stellar rep.)
Let's talk about this Martin's history for a moment: ancestry.com and other cited sources in the eBay ad aside for a minute, did you see anywhere anything that mentioned proof that this specific horn was the one on board the USS California? Is there any actual proof? I didn't see a mention of a photo of the horn on board the ship even--let alone letters of provenance attesting to that fact.
From a sax player's perspective, I'm interested in the finish. It might be the pics, but to me the engraving doesn't seem as sharp as it could be, and the lacquer looks a bit too good to be on a horn as well used as this one ostensibly was. This makes me wonder whether the horn might not be a relacquer job. A high-quality relac, but a relac nonetheless.
Since Martins are heavy horns, and have lots of metal on them, relacquering on them isn't as a big a deal--especially if done well--as on some other brands. And given it's not a Selmer, it wouldn't drop the price significantly. However, when dealing with something that was present during a moment of history, again the buyer would have to make the determination whether or not a refinish would adversely alter the price.
FWIW, IMHO the price is too high. You can get a better model Martin for waaaay less money in original condition. Have a custom overhaul done, and you're still thousands ahead. Again, just MHO. YMMV and likely may.