Moving the pivot point of the rebuilt desk lamp arm back about 75 mm put it at the proper spot:
That required snaking new wiring from the transformer in the base through the upright and out through the boom to the LED floodlamp. I used a random length of speaker cable from the Big Box o’ Heavy Wires, although it doesn’t take much to carry 300 mA at 12 V.
The lamp head now reaches the work area and the base stays out of the way:
It is, we both agree, hideously ugly, but it puts plenty of light at the right spot.