It may be more difficult, but it's probably better for you. Before I went full-time standing desk, I sat on an exercise ball all day for years, and my core strength and sense of balance reflect that.
I hear this a lot. Unfortunately the science does not support the idea that sitting on a ball all day will significantly strengthen your core, but it may habitually force you into a better posture (or it may not - be careful). Functionally you'd have the same effect from sitting on a padded stool without a back.
I'm not familiar with the studies you refer to (and you don't explicitly refer to them so I can't check them) but just thought I'd note that core 'strength' could mean either muscular development or neural development of the control of those muscles.
To be clear there isn't a study done on bouncy balls that I know of (there probably is, I didn't look it up), just based on more fundamental science: in terms of physical adaptation there is pretty much no way to increase either neural or muscular development without an increasing intensity of stimulus, which balancing on a ball will not allow you to do. You will probably gain a small amount of both for the first week or two, but then, absent of increasing stress, your body will stop needing to adapt and stabilize.
I think with your feet wide you enter a pretty stable tripod stance. And you could easily adjust the length of the chair or give it feet. But since, I presume, neither of us has tried either device, it's all academic, isn't it?
Also, having to balance on two axes with the milking stool is much harder than with the chairless chair, which only requires you to balance on axis.