My QDX is now repaired and seems to have quite a hot receiver. As I write at 2:30pm local, I'm receiving stations from NA, SA, EU and Africa on 20m FT8.
My problem was a shorted primary-secondary winding in T1. Fortunately, I used a current-limited power supply when I initially attempted to power-up the newly completed kit. Power supply voltage dropped to zero (with 11V dialed in) and there was no indication on the kit's LED.
There was unmistakably a short somewhere.
While building the kit, I was surprised at the ease with which the insulation could be scraped from the 22g wire used for T1. I think I could have removed it with my fingernail so it was the first component I suspected when I had this problem. I believe that, in the process of winding the transformer, the insertion of one wire scraped the insulation from the winding already placed.
I removed T1 from the board, re-wound it with wire I had available and tested resistance readings again, that were faulty before. Success - no shorts between ground and VCC.
So I applied power and got a fast blinking, then a steady, LED. Success.
Connecting to the PC gave the hoped-for "Device Found" and then "QDX Ready" notification by Windows. WSJT configuration went exactly as described in the manual and signals started filling up the screen.
A brief test transmitting on 20m with 11VDC applied gives 3.5 watts out.
I don't want to transmit for a full FT8 cycle with the small wire now making up T1 but am 100% confident that everything now works correctly. I will re-wind T1 with the proper gauge wire once it arrives.