Treating Room with Rigid Fiberglass (pics inside)

Hey guys, this is my first post in the forum and you all seem to be quite knoweledgable about acoustics. I'm a vocalist and a guitar player primarily, but I've been dabbling in production for two years. I just want some good quality recordings. I've got everything in my recording chain set up and it has become obvious my weak link is my room acoustics. I am currently recording in my walkin closet, but with the door closed the room is excessively bassy, even muddy. The floor is carpet. I want to eliminate all reflections in my room, giving me a dry signal to tinker with in production. Reading around, I've read that rigid fiberglass through a high frequency absorber (maybe burlap?) is the way to go. I'm guessing I should get some thick fiberglass to absorb bass in the corners and evenly spread 2" thick fiberglass to cover the rest of the room? I would also have to cover the inside of the door. Should I keep my clothes inside to further absorb reflections? Also, where would I look to get some rigid fiberglass covered in a material like burlap? Would I have to do a lot of cutting for the material to match the dimensions of my room? I would truly appreciate any advise!

Your closet almost seems like a vocal booth. There are some vocal booths with treatment here and here Here's a good link to building bass traps and broadband absorbers.