Following the advice in
How to get ubuntu 18.04 from windows store if ubuntu and ubuntu 20.04 already installed
I can create multiple instances of WSL distros and run them with the command:
wsl -d foo -u me
Where "foo" is the distribution name and "me" is my user ID. I even can make ones pre-populated with my home directory and the software I want to run. This is very close to what I want. However, I am missing a bit of the functionality one gets if one installs the distribution from the store. In particular, that makes a "foo.exe" file that you can pin to the task bar and use that to open multiple copies of that same distribution just by clicking. I'm looking for a way to create a similar "shortcut" in particular something I can pin to the task bar, drop into a toolbar, or pin to the start menu, or maybe even pin to a context menu.