Hriston
Dungeon Master of Middle-earth (He/him)
Just my interpretation. Both arguments have merit, and obviously the only interpretation that matters is the DM at your table. You're right that there's no rational reason why one should need to occur before the other.
Perhaps I just prefer the second option because it repeats neatly each round, whereas the former must alternate between shoot > swing and swing > shoot, allowing the player to sometimes get OAs, sometimes not. Messy.
I see. For me, the two-round cycle seems the more elegant, as it allows for a full round of swinging and a full round of shooting, with the break being in the middle of your turn when you draw or sheathe your sword. Losing the ability to make opportunity attacks with your sword half the time seems like a small price for what otherwise doesn't seem possible, and remember you could always OA with an unarmed strike with your free hand.