I'm pretty happy with the final result:
The plans suggested using pocket holes for the joins, so I purchased a Mini Kreg jig. Pocket holes consist of a pilot hole that is wide enough that the threads of the screw don't engage. The pilot hole is coaxial with a larger-diameter but shallower hole that can accommodate the screw head. The screw goes through the pilot hole and into the wood to be joined and since the threads don't bite into the first piece of wood the two pieces are pulled together by the screw instead of pushed apart.
There are four pocket holes per horizontal support and 12 supports per stool. I drilled 108 of those goddamned pockets in total.
I actually did the final assembly of the stools back in April. I originally just used 1x4 planks for the seat:
Unfortunately, I did not like the seats. They were a little narrow and I broke off a drill bit in one, so I wanted to cover that up.
So I decided to make new seats. I got a little... experimental. I tried to make new seats out of cement that I could bolt to the existing seat. That did not go well:
I'm just not fast enough making cement or well-versed enough in mixing it to get the proper plasticity. So it ends up being brittle and breaking in my hands, when it doesn't set before I have placed it.
I did get this cool flagstone out of it though:
I need to go at it with the diamond polish pads some more though. I do like that I succeeded in making the red "G" by putting a relief in my cement form then pushing red-dyed cement into the void.
And my many false starts in cement design occupied my summer.
Finally, I decided to use slate tile as the seat, supported by a wood frame composed of 1x2 strips and quarter-round molding.
(A hole saw is superior to a paddle bit for cutting 1 1/2" holes in oak; the more you know)
I didn't want the structure to flex much under the tile (and crack it), so I supported it with multiple layers of wood bolted to the stool. There is a 1/4" of beech to provide a level surface, than a 1/2" of oak to recess the bolts, then 1/4" of oak to support the bolts. I used backsplash adhesive to hold the tile to the beech, then wood glue for the rest of the laminate. All that is shown in the preceding pictures.
After gluing the layers and curing under pressure, I used L-brackets to hold the laminate to the frame. To protect the finished stool in case I decided I didn't like this, I used felt furniture slides and craft-store felt over the hardware. I then slid the stool over the bolts, which fit between the 1x4 seat slats. I put another piece of felt down as protection and used washers and nuts to secure the seat.
Another shot of the finished product:
They are much more comfortable now, though a tad top heavy.
Now I just need to figure out what to do with the wood I have leftover.