There was an EAA pancake breakfast at Lincoln, so I took the DRZ over and partook. Dilly, the local FAA drone, showed up and talked us through how they can help (help? This is the FAA!) with registration of new planes and so on. It was an interesting talk.
In the afternoon, I went back over to the airfield and took the plane up to try and see what's going on with the CHT probe. I discovered that in a shallow climb, I could hit ~6250rpm, and at that point the right hand temperature would climb quickly. If I climbed out harder, I'd be at ~6000rpm, and this wouldn't happen. As the "problem" had moved from the left register on the display to the right register, it's the probe, rather than the cylinder. As the wind was getting quite unpleasant (gusty and crossy), I gave up and parked the plane and headed home.
On the way home I figured out what the problem is... what else happens when the revs go up? The EGT goes up - I reckon that's overheating the metal sheath on the wire, and that's causing the high reading. Of course, I need to fiddle with this to see if that's truly the case, but it makes sense.