A reasonable thing for the flyer to do would be fly over your model as a walk action to engage the rear (if they had enough movement, which they should if they were only a few inches away), then next short action is melee. You wouldn’t get the rear arc bonus, but the model being attacked also wouldn’t get the obstacle armour bonus. However this also means on the retaliation (if there was one) the flyer wouldn’t get the obstacle armour bonus either because it’s not in between them.
The rules felt weirdly laid out to me at first as well, but it makes more sense when you realise there’s not really a ranged phase or melee phase. There’s just rounds and turns. So that’s how the rulebook is laid out. What’s the structure of a round? Alternating turns. On your turn what actions can you take? Lists of actions. Then it goes on to explain how movement works for move actions (as that’s probably the first thing you’ll do), then ranged attacks (the next most likely thing you’ll do), then melee etc. I find the index is actually quite a good index and saves me a lot of flipping around.