Thanks for the suggestions. I ended up returning the x85k and buying the x90l (thanks, @Abeabe ), and it seems better. I put some pics online of my oscilloscope measurements of the x85k and x90l. I measured by putting a phototransistor close to the screen with a black piece of foam around it so I'm hopefully measuring light in a small area, rather than averaging over the whole screen. Here's the Sony 65x85k (in picture mode, with all processing turned off that I could find):
There is some small beating at 120Hz you can see in the x85k. ( each vertical line is 10ms, so a 120Hz artifact will appear a bit more frequently than once ever every line).
Next, here's the 65x90l, similarly in picture mode with processing off:
Sorry for the blurry pic. Each vertical line is still 10ms. You can see the ~900Hz frequency. I think there may be some slower, possibly 120Hz fluctuations as well, but I think it's more minor than the x85k. And subjectively, I notice less flicker on the x90l than the x85k, though I"m less sensitive than others to it.
One other point, when I was in BestBuy looking at the x90l and took a pic with 8x slow-motion on my cell phone, I could see crazy flickering. And I tried to do it at an angle that wasn't picking up reflections from other tvs. At home, 8x slow motions shows no flashing. The tvs in the store were running in demo mode, so maybe they had funny settings or were picking up something from surrounding tvs.
Lastly, here's a pic of the sensor if anyone's trying to do something similar. I took a piece of black foam, cut a small hole in the middle, and stuffed in a Vishay tept5700 ambient light sensor (phototransistor), and then connected it to a 100k resistor to ground. The high 100k value was because I run the tv relatively dim and so the sensor is picking up like maybe 10 lux of light (running a few microamps of current).