Hi Nick and Brian:
Thanks for your input. Here are my comments:
I usually balance the tables as Nick has suggested - in the first example, placing the new player in seat #1, and in the second example, placing the new player on the button and having him sit out one hand (following RROP that a player moving into the button must wait for button to pass).
I think you will agree that the rules do support the above method. When the button moves into seat 6 and seat 8 is due to take the big blind next, seat 7 is due to take the small blind. The rules explicitly set out that the new player enters into the worst position "which is never the small blind" - if we were to allow a player to sit in seat 7 and post a big blind, despite the button being in neighbouring seat 8, I don't think this part of the rule would ever have any meaning because you could always move an incoming player into what would otherwise be the small blind's position and having him post a single big (which is effectively the alternative way Brian mentioned). All I am saying here is that the rules on balancing when taken as a whole seem, at least to me, to support the above "classic" way of balancing because it makes specific mention to the worst position never being the small blind.
That being said, I agree that the "progressive" way is indeed gaining traction, and if it weren't for the fact that the TDA rule mentions "never the small blind" in passing, this alternative way of balancing would appear to make complete sense because it does force the incoming player to post a Big Blind as soon as possible, and it is permissible to post a single big blind.
My original reason for bringing up this balancing scenario is this - I started trying Brian's "progressive" way (i.e. in both situations, seat the new player in seat 7 as BB only with button in seat 6, and then on next hand, new player is SB and seat 8 is BB with button remaining in seat 6) and thought it made complete sense, until I realized that in two particular scenarios that I mentioned where seat 6 is vacant, the player in seat 5 would effectively be acting last as the button not once, not twice, but three times! When the button was in seat 5, he was the button so he acted last. When the button moved to seat 6 for the next hand (which would be empty since you've seated the new player in seat 7), seat 5 will act last again. And then when the button stays in the same position on the next hand, seat 5 will act last yet again! Therefore, in order to get the new player to post BB right away, we have given one player the advantage over the entire table, allowing him to effectively be the button three hands in a row. I'm not sure this is a completely fair trade-off.
So now I'm leaning towards going back to the "classic" way... Any thoughts?