Well...
Once upon a time, I didn't own the LP either, and I had an impossible time finding it through international markets. I asked the very same question, and no more than three people out of Ringo Jihen (our predecessor community - now closed), claimed they owned it - and one of them supplied personal photos.
That was a bit discouraging, but eventually I came across
Shopping Mall Japan. They're a 'deputy' service - a middleman to get you the things you want from Yahoo! Japan Auctions, that Japanese sellers aren't (for whatever reason) shipping internationally.
It's actually not very difficult to get the KSK vinyl that way at all. It's only a question of, how much do you want to pay, or, how long do you want to wait for a lower-priced auction? The cheapest I've gotten away with is 2200yen for a sealed copy, and that's freakishly rare. What used to be the 'norm' (roughly six months ago), was the same seller kept unloading sealed copies for 3000yen each until they basically ran out, and most of those auctions wouldn't even get more than one bidder (I suspect people knew there was a continuous stream and they'd wait their turn). Nowadays the used copies sell for about that much, and the sealed ones sell for 4000-6000yen - this is if you don't want to wait, and it's the price range I encountered when I first started using Shopping Mall Japan.
Whatever the auction scenario is, it's not going to involve eBay (or at least not more than
once every few years), and you always have to take the
fees into account when you use Shopping Mall Japan (in addition to your
deposit). I've won mini-vinyls for 2500yen, and ended up paying around $41 USD after all the fees kicked in. The fees effectively go on a curve that's more favorable toward more expensive auctions, but they really sting if you win a lot of cheaper auctions.