Quick thoughts. The better you swim technically, the less energy you'll expend and you may be able to go further without resorting to breathing on every two. I swim with an ironman athlete and he can do a mile breathing every 3. I peter out after about 300M and I think that's conditioning and age.
You need the air. So breathing every 2 will probably be necessary once you hit some point. This is totally normal. So I think the how to proceed depends on minimizing the cost of breathing. I'm working on the same to breathe on "ones," every stroke for the final leg, or for times when air is precious: before and after turns, in rough water, sprinting to a finish. Haven't mastered it yet and so far, slowing down so my technique works properly on "twos" seems to be the better answer. Still, swimming in busy lanes, sometimes I turn to breath and get a wave of water from another swimmer, so being able to grab the next breath on the other side without losing speed is important.
Anyway - thoughts on breathing
Make sure that you're rotating your head like a kebab on a skewer.
Keep the crown of your head low in the water and pointing forward.
Move your mouth/chin to air, not your eyes.
Grab your breath early, while your recovery hand is behind/below your shoulder level.
Swim flatter with less rotation, which helps keep your platform stable and not sinking.
Focus on your spine and keeping straight posture all the way out the top of your head.
Combining patterns is great. That you can swim bilaterally is a great asset. There aren't any rules. You can setup patterns, but if you feel you need air, take it whenever you need. Also take that need for air as feedback. Are you going too fast? Are you losing efficiency. If you're trying harder and harder, requiring more air, but not going faster, then your stroke is breaking down.