Jeffrey,
Likely what you're feeling is habitual resistance to anything but panic breathing. Most folks walk around in a state of perpetual panic breathing...especially when training. Your body's habitual response to the extra strain of the swings is to do what it does best - panic breath. By trying to alter your breathing patterns you're trying to re-set your breathing habits. (Un?)Fortunately it's a never-ending process...but there are very rewarding milestones along the way which if crossed will make your life suddenly so much easier and enjoyable. The reason most folks don't pursue these skills is because there is no weight measurement, belt or rank involved in improving your breathing. Nobody won a medal for "best breath" or "best nervous system regulation." Work with it, be patient and don't force it and things will get interesting.
As a further expansion on this topic this is one of the things that I find so appealing about the S&S book in general. By stripping it down and making it a near-daily routine you are confining yourself to a box. By constraining yourself in this way you will be forced to find ways to create variety and self-discovery within the program rather than within programS. It suits my experience and training philosophy very well and I am enjoying it very much for this reason. On my "day off" I just cut my volume to 49-50%, drop my average intensity to about 60-70% and work within the breathing, technique and recovery stuff. Lately I've enjoyed playing with the rest periods between the TGUs. Close my eyes, try to breath deep and slow and relaxed as possible, keep on top of my panic reflexes and don't allow them to take over to make my breathing faster and higher, gently reassure my body that all is well and there is no reason to overcompensate, try to slow my heart rate down by tying it to my breathing. The result is that my sessions end up becoming profoundly relaxing and meditative, not unlike the effect of a good Systema training session or a few good Taiji forms. Its funny how we compartmentalize things...I always thought of strength and conditioning as existing within that "panic mode" world that I had so happily left so I felt just a little bit uneasy about it since it was reinforcing bad habits. Needed S&S to kinda hit me over the head that it didn't have to be that way, to see the continuum between all that I did and to realize that there was no excuse to not apply the lessons of other skill sets to this training method. And now I feel the circle is complete and there is no longer an artificial mental divide between these pursuits. Perhaps this is a reflection of the fact that S&S seems much more self-consciously directed to the martial artist than to the powerlifter, bodybuilder or general "fitness" type. I found it spoke to me much more directly than any of the other works by or affiliated with Pavel. Just a little thought I wanted to share. Best of luck playing with your breathing...it can be a very trying but very powerful experience.