Interesting situation Brian. It's very non-standard, there's not a solitary rule that applies to it. You have to use a) best interest of the integrity of the game; b) protect your own hand; c) misdeal rules; and d) substantial action rules... to arrive at a solution. I'm pretty sure there will be some disagreement on this one because of the assortment of rules that apply.
Here's my problem: why wasn't this noticed until after 4 players had acted

? The answer is that for a time period during which 4 players acted we have absolutely no idea what card was in what hand...
THEN we wake up and surmise that the straddler swapped his hand with the BB's hand. And we surmise that the two cards floating on the line are the straddlers rightful cards and the straddler is holding the BB's rightful cards... But how do we know this to 100% certainty if we haven't been watching the cards during the action of 4 players??? How do we know this anymore than we might surmise that one of the BB's cards is mixed up with one of the straddlers cards? And how do we know that whatever happened happened during the initial deal and not later? We have reason to believe it happened later because we have right to assume that the BB was watching the initial deal to see that he got two cards... then he lost track of his hand. That's as logical as him posting his blind and paying no attention to the fact that cards weren't coming to him...
SO, at the end of the day I see this as "two messed up hands". And a messed up hand is a dead hand if substantial action has occured, which it clearly has. While we might say the BB is the most injured player here, he contributed to his injury by not protecting his own hand or speaking up during the ample time he had to bring attention to the problem. I really can't see returning his BB here, and I'd rule both hands dead. In the long run I think this will also contribute to the integrity of the game by teaching players that they must protect their hands and they must speak up promptly if they see a problem. Thanks for a very interesting post.