One one hand, I hate sharing tips with the B.E.A.S.T. crew, because it might potentially mean fewer of these episodes. That said, this is such a great series, and I really hope you guys succeed.
One pearl of wisdom I remember from Scott Manley's tutorials: when you're really far away from your target, the location of the maneuver doesn't need to be precise, but the Δv requires very careful precision. The opposite is true when you're very close to your target, location of the node is much more important than speed changes.
Also, the reason you are supposed to burn half before the maneuver node and half after is because the node assumes an instantaneous change in speed at that location. Since your rocket needs to accelerate or decelerate, you try to average the burn on both sides of the node.
alecmckeown's comments