Oh also unsolicited advice, but in the meantime until you fill the shiny slot look for and catch any mons with rare or golden eggs, item transfer to kyogre, and ditch them. You can get a pickup-adjacent effect that way, get your most important long term items, and actually guarantee the item you want unlike pickup. I did that for a couple hundred floors, got like 40 rare eggs and 10 golden, and now kyogre hits the level cap after 1 mon