I've attached screenshots of all the mods I've added so far, but only the NRaas mods are showing up in the mods detected when the game first opens and working in the game. I've read that I need to enable script mods in the game options, but I can't find the option. I've gone to Options while in and out of my town, but there's no option to enable script mods on any of the tabs. I'm running the most recent patch version of the game. What am I doing wrong???

It doesn't really matter whether they show up in the welcome screen or not, only if they work in-game - which you would find out pretty fast.
There is no "enable/disable mods" option within the game options; closest it comes to is the "run without custom content" option in the Launcher, which I assume disregards all the stuff in the Mods folder, and all installed .sims3packs within the Launcher.

So you're telling me that I've been freaking out about this all day and it's actually working?? lol. Well at least I know now. Thanks!

Yup! If it works, no need to worry You can tell pretty fast if they work, if you don't see the intro video on startup.