Ok, first puzzle solved. I had the two 0603 LEDs reversed.
The silly part is that I had actually built a test rig to make sure this wouldn’t happen:
As trivial as it gets: a battery with a series resistor. By holding the SMD LED against two copper contacts it’s easy to check which side is which. Here’s a green LED lighting up:
Then I got confused and placed all the LEDs exactly the wrong way around – doh!
There are three copper pads. The middle one is PLUS, the other two are GROUND.
Ok, now the RX+TX LEDs blink a few times when plugged in. Onwards!