Good post - brings back unfond memories. I used to swim about like a tricycle missing one back wheel . . .
The speed increase might be due to simply swimming straighter - are you seeing the 30% increase in the pool, open water, or both?
Another explanation could be that your breathing strokes create significantly more drag and/or generate less propulsion than non-breathing strokes. Ideally, there should be little difference, but in reality, head lift, arm drop, dead spot, scissoring, etc. on a breathing stroke are all draggy, slowing factors. If that's the case, breathing every three instead of every two may generate more "speed" just by reducing cumulative drag - i.e., instead of fast-slow-fast-slow-fast-slow, you're doing fast-fast-slow-fast-fast-slow. Might be informative for you to swim at the same stroke rate with a swim snorkel, or if its just a 25, taking only a breath or two over the length (take breathing mechanics out of the equation entirely) and see what THAT does for your speed - if you swim the same stroke at the same rate and see a big speed increase just by taking out all or most of the breathing strokes, that tells you something about what those specific strokes are doing in terms of adding drag or losing propulsion - and why you may be going so much faster by doing less of them in bilateral (every 3) vs. one-sided (every 2).
If we're swimming arcs (much less circles) breathing to one side only, there is more wrong than the breathing pattern - the stroke is bigtime assymetrical - the right half is not mirroring the left half, or the breathing side is not mirroring the non-breathing side. Bilateral may produce a "net" straighter line - there's a veer right for every veer left - but bilateral in a cross-chop just means hassle every other time you breath, instead of every single time, and doing with less air. It probably makes sense to try to even out the stroke so you can swim straight to the next buoy, breathing to either side exclusively - many more respiratory cycles, much more 02, and less fatigue or more speed over the distance.
Swimming in a lane with eyes closed is a quick easy way to check symmetry and line of travel - if you can go 10-12 strokes and stay over the black line - good stuff; if your hitting the lane divider on your 5th or 6th stroke (as I was at one point) . . . to quote Homer Simpson . . . Doh!!! To improve it, what worked for me was just focus on making the right half match the left - closing the eyes for the middle 5 strokes of a length, trying to sense the same rotation, same pressure, same timing etc.- and one-arm drills, rotating and breathing to the nonpulling side - challenging at first, but effective.