-- Last Updated: Dec-20-12 9:23 PM EST --
This is me in the 15.5. Quite manageable if you ask me -;), even though at that time I was still relatively new to white water and you can tell I'm not paddling that well.
I'm taller than you at 6'4" but similar weight at 185 lb or so. You are right that the boat does feel shaky from side to side. I paddled the 16.0 in the same rapids as you see on the video with the 15.5 and I did not see much difference between the two - the 15.5 was a bit more maneuverable and a bit narrower, which I liked better for these conditions. I also paddled the Tempest 165 in the exact same rapids and that is different too - more stable in terms of initial stability (less wobbly) but less final stability too.
Try the Delphin or a Cetus MV - you will like these better from what I read. They have solid primary stability and good secondary. Although if you do feel the Zephyr too tippy, I would think you probably need to stick for now with 24" wide boats like the Tsunami 140 or 160 - they are more stable and probably a bigger cockpit for your preferences there (too big for mine).