Based on the above I figured out that if I first install the Fangamer files to a PC that doesn't have Steam installed and then manually overwrite all the files onto it the update will work. That way I don't have to reinstall Steam every time an update comes out, but it's still a pain.
The next problem I came to was Gamepad support. The game simply does not recognize any of my Gamepads. Not my Nvidia Shield controller and not my PS4 controller. The PC recognizes it, but the game doesn't... Unless I open it in Steam. Then it works. Ugh. So both game updates AND gamepad support is locked behind the Steam wall? Why?
I found this workaround:
"C:\Program Files (x86)\ConcernedApe\Stardew Valley\Stardew Valley.exe" %command%
Using the above under "Launch Options" in steam to make it run the path of the game which means that it won't be running whatever it updates to, and the gamepad will work, but if I try this:
"C:\Program Files (x86)\ConcernedApe\Stardew Valley\StardewModdingAPI.exe" %command%
or even this:
"D:\Program Files\Steam\steamapps\common\Stardew Valley\StardewModdingAPI.exe" %command%
The gamepad will not work in Steam, even if launching from Big Picture mode unless in the properties I de-select "Enable the Steam Overlay while in-game", then it works so I can use the controller to try playing with mods.
However, again, this ONLY works launching from Steam and ONLY if I ALSO install the game from Steam. I can use the above method to run the Fangamer install that is in a folder other than what steam installed, but in that case I am required to have two installs on the same machine which is redundant aside from the obvious situation of wanting to avoid automatic updates that might break a mod.
So, I am still trying to figure out how to play without Steam.
Finally, I tried using JoyToKey to manually set the keybinds and that at least worked, well, sort of. It can't do everything I can do on a console because, for example, there are no keyboard shortcuts for "Open Crafting Menu" and I can't switch items either because, unlike other games that use the mouse scroll wheel to switch between items on a bar (which I can replicate with a trigger button in either direction) this game has me pressing 1 through 0 which I can't do. and even if I could, the game changes what button does what when menus are open.
*sigh* So, in case I missed anything, does anyone have any other ideas on what I can do to be able to play this game without steam? I've been at this literally all day.
EDIT: I made some progress. Turns out if, instead of installing anything with Fangamer disc, I installed fresh with Steam and ran it once from Steam with the gamepad working I can then run it without steam afterwards and the gamepad will work, however, so far this only works for "Stardew Valley.exe" and not "StardewModdingAPI.exe". There doesn't appear to be any way to run the Fangamer install without launching through a steam game installation's launch options and no way to run mods without running through steam specifically. So far. I'm still trying.