I thought that might be the case but since aircraft could fly over an unfriendly neutral if they attacked it
Depending on what you mean this is or is not correct. When you say “fly over” if you mean they can fly into the unfriendly territory during the Combat Movement phase and attack it in the Combat phase and then in the Non-combat phase fly out then that is correct. If you mean some units attack an unfriendly neutral and other air units fly into and out of the unfriendly neutral during the Combat Movement phase to attack elsewhere that is not allowed if this is the first time the unfriendly neutral has been attacked.
A major sticking point among my friends in playing Axis and Allies is the wait time between turns.
What about having a combined purchase phase for all players?
And use markers for each IC (like fleet markers) to position purchases awaiting placement.