While technically not the way the manual tells you to do things, this is how I normally make sure everything that needs to be done gets done:
1) I roll all AA Guns for every battle. That includes those flown over to get to the battle if necessary. By rolling them first, it ends any confusion as to whether or not they should fire. (It also cuts down on remembering what flew where and how.)
2) I roll all Battleships (and Destroyers) that are bombarding. If this ends pre-initiated battles, then I make adjustments at that time. It also helps you remember if that BB/DD is engaged in combat, or free to perform their bombardments because the enemy units, if present, are still there! (This is also the time I roll any Strategic Bombing Damage, it’s convenient for me because I can make white dice bombers, red dice battleships and blue dice destroyers if I have the technology for them.)
3) I roll all naval battles (submarines first, get the casualties assigned, then everything else. Attacker then Defender.) This solves issues of forgetting that transports were off loading into an amphibious assault and rolling out the battle before making sure the naval battles were completed.
4) I roll out all the land battles. Since all the AA Guns and Bombardments were taken care of in Steps 1 and 2, I don’t have to worry about remembering to deal with them later.
This may or may not work for you, but it works for me and, since you were experiencing issues about who gets to do what in certain circumstances, I am hoping these four steps will help prevent further such issues from arising.