I did a quick search through my paper database
and came up with 24 papers I've tried that meet your 100% Cotton, Matte, requirements. Of those, using my printer (Canon iPF5100) and my test image, the ones I measured the deepest blacks on are:
Hahnemuhle Photo Rag
Hahnemuhle Photo Rag Ultra Smooth
Hahnemuhle Museum Etching
Hahnemuhle Photo Rag Bright White
Moab Entrada paper is nice too and has similar blacks to the above. All these papers vary quite a bit in paper tone and texture. The Bergger PN33, for example, is hideously ugly due to its texture. The Photo Rag Ultra Smooth, on the other hand and as its name suggests, is quite smooth. Entrada has a nice, light, texture.
You can download the database and do your own filtering to come up with a candidate list of papers to try. All of them are generally available in small sample packs with a variety of papers so you can try them on your own to find one you like. I can't recommend a personal favourite from this list as I don't like printing on matte paper
If you really, truly, want rich blacks you should take some of the baryta papers for a spin. They're "glossy", but the blacks are amazing.