@uhoh As you might have guessed, I keep trying to get the "simple" two-body-with-zero-mass-satellite problem cracked before moving on to more complex transfer problems. It's putting up quite a lot of resistance so far!

The most valuable contribution so far actually came from the math people:

Which combined with the intuition that bi-tangential transfers are efficient somewhat settles the planar case.

@SE-stopfiringthegoodguys bravo! I have up votes on both question and answer which means I've seen it before, but it could be quite some time ago. I remember understanding that i was in the presence of beauty even though I couldn't take it all in at the time.

I'll take a look again soon when I've got a moment to clear my head, and see if I can get closer to understanding it. Thanks!