1. Replace the "PhysX_SystemSoftware.msi" file from steamapps/common/Deadly Premonition The Director's Cut/redist with this version.
2. Select Proton 4.11 as the compatibility tool and run the game once, exit at the launcher.

3.     wget https://gist.github.com/Neodamode/65d23eab40b06193835402097636cb97/raw/2cdcd20c201f3b57f55f03d30320ac660e92a64d/vc1decoder.verb
   

4.     protontricks 247660 -q quartz qedit devenum wmp9 /path/to/vc1decoder.verb
   

Edit to wherever you have downloaded "vc1decoder.verb". If protontricks hangs indefinitely installing wmp9, open a new terminal tab and run "killall cmd.exe" and it should continue. 5. Optionally add the "PROTON_USE_D9VK=1 %command%" launch option for better performance (haven't tried it myself).