Alright so I currently have the following mods installed: 001 Project Weaponry, ADAM, CNR, NCRTrooperOverhaul, Readius_NV, TheLozza's Gasmasks, and Factions Reloaded Raiders v2. I've got more but those are the only ones I have enabled and on the startup loading screens the game will say I have received my Mercenary and Caravan packs, then it's a black screen with music still playing. I'd appreciate all the help I can get.

It seems that you do not have any mods that effect user interface so we can rule out that as a problem. It may have something to do with a corrupted file during download of both DLC packs. So I would suggest that you verify the integrity of you game cache in steam. This might fix the issues with corrupted files.
If it is not a problem with your game files, it may be a mod that installed wrong or overwrote something. Though you do not have many. What you can do is try running a vanilla game (no mods) and see if that works. Or you can go down the line and uninstall each mod and test that way. Really slow that way.
Lastly, you could delete the data folder and then reinstall all your mods again. And you don't have to many installed so you should not have to take up too much of your time with that whole process. Good luck and I hope this helps. Please ask if it does not and I will try to help.