I've only had one of the 10mm Kagayakis (3k) and it didn't warp because I permasoaked it, but I would've thought that the Chosera base would be sturdy enough to prevent it, yep.
Another perhaps even better and still very cheap option though might be to use a bit of roofing slate, which you should be able to get either free, or just a dollar or two. Cut it to size, which you can do with any kind of handsaw, and flatten with an atoma or sandpaper. That definitely won't move around in a hurry, and has the added advantage that you can hone a razor on it too of you want - might be a good final step before moving onto the 12k. I've made a lot of whetstones out of Aussie slate and works quite well, if I was still there I'd pop one in the post for you.
Haha. You're very kind, though there are loads of people here who've been at it a lot longer and know a lot more than me!