Make sure that everything downloaded correctly before you try these methods. Check if "Eternal Damnation (Launcher)" appears in Workshop menu in-game.

Workshop ERROR Solution:
Using the methods below migt cause a workshop ERROR to appear at some piont, but don't worry it most likely means that I've updated the mod and game can't update its files because it's currently running. If it ever happens just launch the vanilla game and wait for the update to download.

1) Go to POSTAL 2 files directory and open WorkshopContent folder.
2) Find a folder 2006427295 and Play Eternal Damnation.bat file inside it.
3) Make a shortcut to it on your desktop and done. Use it to start the game.

1) If you have Steam Edit I assume you konw more or less how it works.
2) Use Edit Launch option and Add New
3) Setup the config like this:

Executable:Arguments: Working Dir:
1) Create a new "non-steam" game shortcut in your steam library for POSTAL 2
2) Right click on your new shortcut in steam library, go to Properties,
click Set Launch Options and there add this config.
(You can actually skip the first step and just add this config into regular POSTAL 2 in your libaray but you'd have to remove/add the config every time you wnat to switch between P2 and ED.)