I can't asnwer the question totally, but I can say surely that the 3rd street tiebreaker would have to be suit and not seat position because it would put Seat 1 at a disadvantage because Seat 1 always gets the first card dealt.
Dang! I should have figured that one out on my own. We never play dedicated Stud, just during Dealer's Choice so we move the button each hand to make it easier to keep track of when an orbit is complete.
But that begs the follow up question of why suit isn't used for tie breakers on other streets. Theoretically, Seat 10 would have position on the table more often than any other seat if the button is stationary.