The difference is that you are thinking about orbits fully outside the gravitating body (the star, planet, or moon). In contrast, objects in a galaxy are orbiting inside an extended mass distribution. This means more distant objects feel the gravitational influence of more mass below them.

> Actually, I've just looked up the moon's orbital velocity at 1km/s and low earth orbit as 7km/s so that's the complete opposite of what the simulation implies, which definitely requires prograde burns to increase apoapsis.

Both are correct. You have to speed up to get to a higher orbit, and yet that results in you moving slower on average! As I noted in another comment, that is very interesting because it means gravitational systems have a negative heat capacity (adding energy cools them).