These positions are tricky so I'm going to post my thoughts with the disclaimer that they may be way off. I think we want to hit those checkers. White is going to have a reasonably timed back game no matter what we do, and in these situations if there's no chance of him crunching, the next best option is often to hit as many checkers as possible to try to "over time" his game, which lets us finish bearing in/start bearing off while he's on the bar, and also hopefully win more gammons/backgammons. Which brings me to why I asked about where the cube was. With the cube centered in a money game our gammons are worthless, and we probably win 40-50% gammons here, and so while people have a tendency to overdo the whole "double to activate gammons" thing, here I think it's enough reason to turn the cube.
Can white take? I'm not sure. The reference position I'm familiar with is that when Black has all his outside checkers on the 6, 7, and 8 points it's a borderline take/pass if white has good timing. Compared to that reference position, black will probably still have 3 points to clear (6, 9, and 11), and due to the gaps between them these will probably be a little harder to clear than the 6, 7, and 8 points, which would suggest take. However, white could get all of those blots picked up and black could clear one or two of those points while white is on the bar. I think the gaps between the points to clear are a bigger disadvantage for black than the blots lying around are for white, so I would reluctantly take.
I was wondering the same thing but never came to a conclusion. I've looked at the analysis now so hard to say for sure what I would have done. But I would definitely be less excited about doubling at that score than for money. The boost in gammon value (from 0 to 0.5) was a big part of how I justified doubling in the first place.