I figured it out... I think.
This issue happened before: https://bugs.winehq.org/show_bug.cgi?id=40240 https://bugs.launchpad.net/qemu/+bug/1658141
The Windows crash message was a bit different but the host had similar MSR_* errors on the console.
The workaround then was to run:
echo 1 >/sys/module/kvm/parameters/ignore_msrs
But I set up an init.d script to get it to survive across reboots and unfortunately that script's dependencies were incorrect so, at least recently, it got run before /sys was mounted. But not always. This explains the sometimes puzzling and somewhat inconsistent results I got. It also explains why a simple reboot on the 27th broke ntdll:exception.
Had I noticed the "/kvm/.../parameters/" part of that path I may have realized that the right way to make this workaround permanent, at least on Debian, is to do:
echo options kvm ignore_msrs=1 >/etc/modprobe.d/local-qemu.conf
But, unlike before, that's not entirely sufficient: it does not work with QEmu 3.1; one has to upgrade QEmu to 5.0-14. I have done that on vm3 and vm4, restored the kernel to the latest 4.19.0-13 (it works with 5.9.0 too), and I have rerun WineTest on w864, w1064* and w10pro64.