I like these thoughts! 6 choices per pick might end up feeling overwhelming for new users, since the pieces are pretty complicated
Seeing ahead, interesting idea- so you'd be able to see twelve total options at once. Could be cool! And could have pieces modify that ability, and let you see more, or less for some other benefit. Has a similar issue danger of overwhelming but i like it
I like investment strategies in autobattlers where you have gold or can invest in upgrading the "shop" which modifies rarities or changes the pool of picks in some way. Like in auto-chess games you'd get a higher chance for high rarity cards, and in luck be a landlord there are certain pieces that make rare things more or less likely. (some gem and cats i think) The one off choices you have here just feel like insta picks and unrelated to strategy, where as in luck be a landlord you might not want to get more rare pieces cause you are trying to find a certain common piece.
Fun stuff to think about :)