Thanks for the eBay links. I had already searched there, but for some reason none of those offers (not even the worldwide ones) had appeared on the German site.
Are you sure it isn't the tripod mount on the camera that is loose?
Funny, I just tried putting in the screw without the plate and the bottom of the thread broke loose, despite me exerting only very moderate force. The thread itself seems to sit tight, but it's hard to tell for sure, and I'll certainly have it checked.
Have you tried any padded plates?
Yes, the original Induro plate has some rubber texture, and it does seem to be superior to the RRS plate.
An RRS representative suggested to me flexing of the camera body might be the cause of the problem. I wouldn't have thought of it myself (this is supposed to be a flagship DSLR after all), but from the looks of it, it doesn't seem unlikely at all.
Any other K-5 users here who have experience with tripod-mounting?