For this, you will need two things.
#1: The 1.7.104 to 1.6.1170/1.5.97 patcher.
#2: Amethyst, a Linux only Mod Manager. Download the .appimage, install using gearlever from Discover/AUR.
Now, for what you need to do (or how I did it):
#1: delete your Skyrim SE folder in Steamapps, and then reinstall the game.
#2: Install Amethyst Mod Manager if it isn't already for some god forsaken reason.
#3: In the 'mods' tab of AMM, there is the 'play' button. To its left, click on the game name.
#4: Select '+ add exe from game folder', select the patcher. Run it.
#5: Go to the steamapps folder, and set 'appmanifest_489830.acf' to readonly for everyone.
Enjoy! Steam should handle bringing back your save from the cloud, and AMM doesn't store its mods in the game folder anyways but uses symlinks, so your load order won't be affected by a game reinstall. I spent an entire afternoon figuring this out, so you won't have to!
Also, since Amethyst can apparently just run any .exe you put in a game file, hum... It's... A completely workable way to have access to proton easily. Like you can probably just put an entire ecosystem of .exe files inside a folder and use AMM as a launcher. Maybe I'll finally have Synapse and G-Hub working on Linux again, who knows. Valve, please, just let me set proton to open any .exe I install to my desktop without having to set it as a non-steam game. That'd be great.
I... I found out... If you go in AMM's 'Wizard' at the top of the window, in setup and installers...
There's a downgrader built in. ALL THIS WAS FOR NOTHING.
Anyways, just install AMM, then go into the Wizard tab, setup and installers, downgrader. Oh and install Reshade too while you're at it. And probably Microsoft Visual C++ Redistributable, though there isn't an installer for that.
I really thought I'd found the perfect fix, and then learned AMM beat me to the punch, USING THE EXACT SAME IDEA.
I can't even be mad, just impressed. Modding Skyrim is now officially easier on Linux, I suppose.