It's already randomized.

Would love to have the option to tell my AI either not to wait for an action to be finished (like some card draw animation if you don't care about the result) or delay a certain time before doing the next action (some kind of additional wait-action to resolve card-IDs of summoned minions by deathrattle-effects)

Actually it doesn't always wait for animations to complete, and it's often bad. I saw many times when, let's say, opponent has two cards on board, bot kills one, then starts to attack another, but it gets moved after first is dead, and bot seems confused.
Also sometimes he tries to attack wrong target after Sludge Belcher is dead, but the small taunter hasn't appeared yet: he tries to attack another target but can't.

UPD: Much alike to the first case behavior is with some minions like Vodoo Doctor: bot plays the card, aims healing effect on the spot where another card was, but it got moved a bit, so the bot gets confused for a couple of seconds.

UPD2(my pure speculation): I understand, that could be due to Position allocated to Card object refreshes only every two seconds or so . Maybe add some "offset" value for a number of cards to add to Position once it decides to play the card.