With a combination of WSL 2, Ubuntu 18.04 LTS and xming I was able to generate the gateware (from Windows) for Artiq 5.7. Generating the gateware takes about 10-15 minutes.
Most of the steps are as above, here are the most important differences:
Get WSL 2 (1 doesn't work). I can confirm that this works with Ubuntu 18.04.5 LTS.
To install Vivado I used xming. After xming installation in Ubunut you have to execute
export DISPLAY=$(cat /etc/resolv.conf | grep nameserver | awk '{print $2}'):0
( https://superuser.com/questions/1476086/error-cant-open-display-0 ). I start xming with xlaunch with "no client" and "no access control".
After running the toolchain I had to zip the files, otherwise I couldn't get the folder out of WSL. At the moment it is not possible to bridge a USB device to WSL. It might be possible to directly reference the WSL filesystem when flashing from windows, but I haven't tried that yet.
Useful things:
You can execute
explorer.exe .
inside WSL to open an explorer window. You can use /mnt/c/Users/... to reference files in Windows.