OK, so the first prototype is complete. And it worked... second time around.
Nasty and uncleaned. Can you read any part number on the left hand SOT-23 device?
Note to young players: DO NOT leave your last container of solder paste open and in a hot workshop for a few weeks and expect it still to be useable.
I tried mixing it with some flux and pounding it into a paste, but (after a lot of trying) it was a lost cause. I ended up soldering these my hand with a soldering iron.
First test showed that the voltage across the input was 3.3V and did not vary with the pot.
Second note to young players: Always check the exact datasheet for the chip. The TI datasheet (which comes up first on Google) shows the pinouts for the TL431 and the TL432. These differ only in that 2 pins are transposed in the 432 (and I have a 431, right?). OK, so I have an AS2431 which just happens to follow the TL432 pinout :-(
Fortunately the fix is as simple as taking the device off, bending the leads around and placing it upsidedown on the board. I say "simply", but the leads get even smaller as you approach them with even the finest tip pliers you have.
And then it works! The adjustment range is 11.32 to 15.02V. That range is a little different to what I calculated, but is fine for a nominally 12V device.
Third note to young players: Make sure you get the connections to the trimpot around the right way. I wanted the voltage to increase as the pot is turned clockwise, but it's the other way aound. Sigh. I read the datasheet and I thought I had it right. And it's really tricky to probe the tiny pads on these things. Oh well, I have to redesign the board to handle the AS2431 pinout, so I can change this too.
Fourth Note to young players: If you're going to breadboard a circuit and you need to use an SMD device, use one in the same package that you plan to use in the final design. I used an SO-08 TL431 in the breadboarded test (because it was easier to pull out of my collection of parts) and the SOT-23 one for the final design (because it is smaller). If I had used the SOT-23 part originally I would not have made the major mistake on this board.