Stroke technique for freestyle with breathing on the same side

I normally swim with bilateral breathing (one per 3 strokes). Every time I try breathing to the same side (one per 2), I feel less good about my strokes, especially my arm opposite the side I breathe. It is hard to capture what I feel, but my technique is different in these cases. I never get to fully turn my head towards the bottom of the pool, and I also sometimes struggle to breathe properly out before the next stroke, so I often dump all the leftover air through the mouth as I turn for the next breath.
Besides breathing, it feels as if my arm opposite the breath is strained a bit too much: I tend not to be able to bend at the elbow as I normally do.
How should I adapt my technique from 1-in-3 to 1-in-2? Thanks for any suggestions

submitted by /u/LeoHerzog
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