I installed the mod and it says right at the main screen that 3 Mods are missing and required for it to work, but it seems to run fine, although every mission I embark on no Advent reinforcements ever show up even though it says "Reinforcements Imminent" for x amount of turns. There is very little to no challenge as the missions are ridiculously easy.

Anyone have the mod working as it should, or should it be advisable to just get the Steam version which seems to work much better with the Mods?

The LWOTC mod actually requires *four* mods from the Steam Workshop to work without issue, all of which are easily downloaded for offline use by utilizing the website Steam Workshop Downloader.

The following four Workshop mods are required:

Better Second Wave Mod Support
WotC: robojumper's Squad Select
[WotC] Mod Config Menu
[WOTC] Revert Overwatch Rules Change

See instruction #5 on the installation wiki for LWOTC here for the link: https://github.com/long-war-2/lwotc/wiki/Installing-Long-War-of-the-Chosen

Open all four mod pages into separate tabs, get those zip files from the Downloader site, unzip them into their own named folders like you have for the LWOTC and CommunityHighlander ones, put those folders into the 'Mods' folder, then enable them in the config file as usual (ActiveMods="blahblahblah").

Now you can play LWOTC offline without issue.

The steam workshop downloader usually has a cached old version of all the mods, that may or may not be up to date.
Use catalogue.smods.ru/game/xcom-2/ instead.