.... I captured sessions with USBPcap, but I think stuff must be being dropped, as what I get makes no sense
Turns out it is all in there. I hadn't realized the URB_INTERUPT packets contained reports too. As can be seen in the captured data file
https://staff.sharcnet.ca/tyson/hidff3.cap
it is brutally simple. When fedit.exe starts, you see
7f - Parameter Block Pool Report 9A - DC Reset 99 - DC Stop All Effects 7e - Device Gain = 255
and it is the "stops all effects" that shuts down the autocenter. When it exits, you just see
9A - DC Reset
and it is this "reset" that restores the autocenter.