Is there a way to write a Scatter that avoids the explicit broadcast, or do you know that's not possible? (IIRC you mentioned that Scatter can't do this without the explicit broadcast, though even if it could, this approach is much more favorable to maintain our sanities. I'm not sure my mind could survive another descent into Gather and Scatter.)

I thought about this briefly and decided (a) I couldn't think of a better way of using scatter to do this, although I am not completely certain given how complex scatter is, and (b) this fixes David's immediate problem. So why not check this in now and revise it if we come up with a better way?