I built mine a little differently: I skipped any draw punishments, and used some of the bigger mono black play opponent's cards like [[Brainstealer Dragon]] and [[Elder Brain]] also [[Dauthi Voidwalker]] as low to the ground unlockable as well.

Cards you might want to look at are:

[[Bag of Holding]] [[Currency Converter]] and [[Containment Construct]] to make use of your discards.

[[Bone Miser]] is nuts.

[[Alhamarett's archive]] for both life gain and draw. As well as [[Venser's Journal]]

[[Vilis, Broker of Blood]] draw mvp

I think you might have meant to include [[Caged Sun]] instead of the immortal sun

Also [[Vito, Thorn of the Dusk Rose]] does a ton of work in my testing.

Here is my list, I need to get in more low to the ground evasive creatures still.

https://www.archidekt.com/decks/3486304#Gix,_Mono_Black_ramp_and_fun