Actually, it's quite easy. Not quite
as easy as on Windows, but easy enough.
https://github.com/redmcg/wine/wiki/Wine has been mentioned multiple times already, and it
does work. The important thing here is to use
winetricks 20190615-next or higher; the earlier versions currently shipped with most Linux distros
seem to do their thing, but Elite won't run. The wiki has links on how to update your winetricks.
Using the up-to-date winetricks, do the dotnet40 / win7 thing as described in the wiki (using
WINEPREFIX=~/.steam/steam/steamapps/compatdata/359320/pfx). For me, winetricks dotnet40 win7 was all it took. Fire up Elite Dangerous on SteamPlay (using the latest Proton of course), and you're set.
As for ED:MC, follow the "Running from source" instructions as that's really the easiest way to get it running -- sudo apt-get install python-iniparse python-requests python-tk git f
ollowed by git clone https://github.com/Marginal/EDMarketConnector.git ~/.edmc or whereever you want to install it).
Then,
manually set up the journal directory:
mkdir -p ~/.steam/steam/steamapps/compatdata/359320/pfx/drive_c/users/steamuser/Saved\ Games/Frontier\ Developments/Elite\ Dangerous
Add a link to your desktop that runs ~/.edmc/EDMarketConnector.py and you're good. (Check in the ED:MC configuration that it's pointing at the journal directory.)
I raised an issue with the author of ED:MC that the "Running from source" / directory setup part should really be a part of ED:MC's Installation & Setup documentation for Linux, but that hasn't happened yet.