Well, it turns out that 1/8″ hexagons are ridiculously small, even with a finer needle.  Regular quilting fabric is just too bulky and fray-prone for the necessary 1/8″ seams.

I’d give it a shot again with a cotton lawn, but I don’t have any on hand or plans to acquire any soon.

There’s likely a good measurement between 1/8″ and 3/16″ which yields a small hexagon, but not one that’s impossibly small.  I’m not sure I care enough to figure out what it might be.

The 3/16″ hexagons are growing on me, though.  So cute and not really fiddly at all, with a little bit of practice.