Here is what I found!
Right click Garry's Mod in the Steam library and choose "delete local content." Then go to your "Program Files (x86)/Steam/SteamApps/[username]/" folder and delete the "garrysmod" folder inside of it. Reinstall Garry's Mod and ensure that you see "GarrysMod" folder inside of your "SteamApps/common/" folder. Verify game cache after running it to make sure everything downloaded properly. There should no longer be a garrysmod folder in your "/[username]/" folder.
I'd also recommend opting into the SteamPipe betas for all other Source games. Right click your source games and click "properties," then go to the "betas" tab and choose the drop-down arrow and select "SteamPipe Beta." Close the window and start the game. It'll ask if you would like to configure the game for the new system; choose yes. After it finishes updating, and you have done this for all source games, delete all the folders in your "SteamApps/[username]/" folder. It should be empty. Verify the game cache of all of your Source games. The "[username]" folder should still be empty, but all your Source games should now have a folder in "common." Episode 1 and 2 of HL2, as well as Lost Coast, will each have their files inside of the "Half-Life 2" folder inside of "common."
You will now be able to mount your content to Garry's Mod. L4D2 and CS:GO content is still broken, and CS:S content often conflicts with CS:GO content. Some filepaths are messed up for sounds, textures and models as well, resulting in some addons/maps having borked content. This is normal and will be fixed shortly.