...single player raising and stealing...
Actually, there's no need to raise. Regardless of position, if all other players are missing, their hands are automatically killed, so the pot goes to the one player at the table with live cards, even without bothering to push chips forward.
I think Bill's 1 minute per hand is much too long. Consider that during normal 3 handed play, unless someone goes into the tank, if it goes all the way to a river showdown, the hand will take about a minute.
Similarly, your 1BB+1SB per minute solution is too fast. You gotta remember that we're talking about THREE hands - don't forget the third hand per orbit where the player is the button. So you're suggesting 20 seconds.
Consider a hand where all 3 players are present, but get garbage. I'm guessing 30 seconds is about an average duration. After all, how long does it take a dealer to wash, gather, square, shuffle and deal 2 cards to 3 people? 20 seconds? Add a few seconds for those players to look and fold, and you're looking at 30 seconds per hand.
For these reasons, I suggest taking the blinds and moving the button every 30 seconds - without need to actually shuffle and deal.
On a side note, suppose the one player seated is short-stacked, with less than one SB. Does the BB get the side pot, or do both blinds keep their excess? Since both blind hands are dead, I'm thinking the BB should not earn the excess from from the SB, but is there a TDA rule for this?