Using my trusty analog caliper, I measured everything prior to posting the OP.
Did it again. If you want photos, lemme know.
For both the Miyata and GF, the orig stock seatpost has a OD of 27.17.
The Satori is 27.22.
One reason the Satori may not fit is that has quite the thick paint job. Also, it has a matte surface; it is not the std "silver smooth" that one normally sees.
On Amazon the most common size seems to be 27.2. That's where I got it from.