I replaced R359 with a 5k pot with 1k resistors on each end. I replaced VR122 with a 1N4578A-1.
Last night, I tweaked it with the DAQ6510 attached to relative stability (I like the graph on that better). Then I let it run overnight, and connected the 34465A across VR122. I let it run for a while with small adjustments until I got it around 7uV PP on the short side (5 minutes or so), and a little higher if I let it run a long time.
The attached screenshots are how it performs after that adjustment, but not substantial warmup time.
Now, I'm going to let it warm up a lot longer, and see how adjusting the R359 pot affects measurement stability. I'll attempt to get it as stable as possible, within the limits of adjusting R359's value. If I get that to a reasonable stability, I'll pull out Funky R359, measure it out of circuit, and replace it with the closest resistor value.
Thanks,
Josh