I know that one of the super mutants is supposed to drop a holotape so I can access the front door in the Military Base. I also used the Radio to lure the super mutants away by giving them bad coordinates and got 1500 exp, but nothing beyond that happened besides me getting the experience. The door remains closed, and none of the super mutants had the holotape.
I did the sidequest for the Thieves Guild for the electronic locks and I fear my lockpicking is too low to open the door, at 41. I have tried about 50 times and the door refuses to open.

I am at a loss as to what to do. I really don't want to start over, because I'd have to go through the entire game all over again and I'm extremely close to the end.

Edit: SOLVED!

IIRC you don't really need to enter the Military Base to complete game, although I can be mistaken.

BTW, are you using any mods?

No mods

Also I checked, unfortunately you need to destroy the military base and kill the master to end the game.

I'm extremely far in, plus I got the Alien Blaster and upgraded power armor, and I've done all the sidequests. Having to restart would be... exceptionally painful so to speak

Hmm...if none of the Super Mutants guarding the entrance have a holodisk containing the enty code, it sounds like a bug.
Maybe reload from before you entered the area?

Or try using the code - KODE 010597 - without having the holodisk.
The door should also be pickable with enough skill.

Well in my genius I saved AFTER I had won combat, so I don't have an earlier save to go back to.

I booted up the game and checked the door again. There's no code to enter manually unfortunately, it just tells me I need a code to unlock the door. I tried using electronic lockpicks but it said I am unable to unlock the door many, many times. I think my lockpick is too low, but I don't know of any other ways to gain EXP since I've done everything else.

Edit: Oh thank god. I had a level up I hadn't put points into yet. I chunked it all into Lockpick and opened the door. Thank god!

Good to know that it's possible to get in with a high enough lockpick skill :)