(I was hoping someone would say "abilities". The grammar of it now is just extra borked. I also can't help but feel that this would work better with pairs of people, and on a better medium for real-time conversation.)
What about "Experimental Charm?" The term "charm" can refer to a spell (referencing the enchantment part), as well as a physical object believed to hold special powers (referencing the artifact bit). The issue I see, though, is confusion with the already-present term "charm" in MTG that refers to a modal spell with three choices.
Let's see... discard and caring about how many cards you have in your graveyard is B, while caring about card draw and adding U is, well, U. The ability lockdown probably fits best in W, but if we want to keep it to two colors, I don't think it would be too terrible of a bend in U. Given that this can be a very potent mana rock, I'd suggest {3}{u}{b} or {2}{w}{u}{b}.
Ok: Experimental talisman /3{u}{b} Enchantment. {1}, {t}: This enchantment becomes an artifact until target player has exactly 1 card in hand. Whenever you draw a card, ad {u} for each 2 cards you have in your graveyard. As long as Experimental Talisman is an enchantment, creatures cannot use non-mana abilities.
Jewel of the Deep {3}{u}{b} Enchantment. {1}, {t}: This enchantment becomes an artifact until target player has exactly 1 card in hand. Whenever you draw a card, add {u} for each 2 cards you have in your graveyard. As long as Jewel of the Deep is an enchantment, creatures cannot use non-mana abilities.
Flavor: Rumors say it belongs to an ancient and terrible entity that dwells in the deep ocean. And anyone within its presence can feel immense dread that emanates from the jewel.
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{1}, {t}: This enchantment becomes an artifact until target player has exactly one card in hand.
Whenever you draw a card, add {u} for every 2 cards you have in your graveyard.
As long as CARDNAME is an enchantment, creatures cannot use non-mana abilities.
Experimental talisman /3{u}{b}
Enchantment.
{1}, {t}: This enchantment becomes an artifact until target player has exactly 1 card in hand.
Whenever you draw a card, ad {u} for each 2 cards you have in your graveyard.
As long as Experimental Talisman is an enchantment, creatures cannot use non-mana abilities.
A suggestion:
Jewel of the Deep {3}{u}{b}
Enchantment.
{1}, {t}: This enchantment becomes an artifact until target player has exactly 1 card in hand.
Whenever you draw a card, add {u} for each 2 cards you have in your graveyard.
As long as Jewel of the Deep is an enchantment, creatures cannot use non-mana abilities.
Flavor:
Rumors say it belongs to an ancient and terrible entity that dwells in the deep ocean. And anyone within its presence can feel immense dread that emanates from the jewel.
With the amount of text and the shift from Enchantment to Artifact in regards to the thing involving the non-mana abilities I would say Rare
https://www.artstation.com/artwork/stones-study
((Ok, were starting a new one.))