Can mods work with the GOG version of Fallout 3, and if so, how? [closed]

I just performed a clean install of Fallout 3 GOTY edition (version 1.7.0.3) on Win10. I want to use mods with it, but can't get a single one to work. It might be important to know that I got it from GOG, not Steam.

I have tried to follow numerous online guides, but none of them helped. I never see any error messages or crashes, the game just starts up with no mods present no matter what I do. All of the guides I could find were for the Steam version of the game. Any time the guides referenced a Steam-based file path, I changed it to my best guess at the equivalent path on my machine, but otherwise I followed the instructions as stated.

To make matters worse, most of the guides I found contradicted each other or even themselves. For example, some said to use Fallout Mod Manager and not bother with Nexus Mod Manager, while others said to use Nexus Mod Manager and not even install Fallout Mod Manager. At this point, I've tried most combinations of Fallout Mod Manager, Nexus Mod Manager, Fallout Script Extender and LOOT. Also, some of the guides were very old and included steps for dealing with obsolete features like Games for Windows LIVE or UAC, which did not seem to apply to me. It's also very possible that some of the changes I made for one guide inadvertently caused problems for my attempts with later guides.

The actual mods I was trying to use tended to be from the group of all-time most popular on Nexus Mods, so they should be relatively stable and trustworthy. I did notice one other weird thing that might or might not be relevant. Multiple guides said it was important to start the game once before doing any modding, so that a base ini file would be present. I did that, and changed a few game options during that first game, like HUD color. After my (failed) attempts to install mods, when I checked the game options, the HUD color and other options were always set back to their default values.

How can I get mods working with the GOG version of Fallout 3? I'm willing to uninstall everything and start from scratch at this point if that would help.

EDIT:
I intentionally did not list the exact steps I took. In addition to being really really really long, I thought they would be too specific to help anyone else. And I might want to change up my mods in the future anyways. This question is intended to be "what are the general steps for installing mods with the GOG version of Fallout 3", not "how do I fix my specific setup".

In particular, is there one mod manager that is known to work well, or one that should be avoided, with the GOG version of the game? Are there instructions that show up in guides that are obsolete and now cause problems (possibly having to do with Games for Windows LIVE) or that are somehow important for the Steam version but end up breaking everything if you follow them for the GOG version?