Sometimes just talking it out is all that's needed, so while at work this evening, I started sketching it out, and had a eureka moment.
So picture, as I described, a 14ga extension cord cut in two and stripped. Let's tie the greems together. Let's tie the whites together. Now lets screw the blacks into the two ssr load terminals, right? So without any additional anything, I plugged a work light in to the female, then plugged the extension cord male into the wall. The LED worklight was on... but dim... if I connected the triggers to the ssr, and energized it, the little red light came on, and the worklight glowed at 100%. Weird, eh? Thst's why I thought "bad ssr". But as I was sketching a better drawing, and labelling each item, I wrote "14ga block heater cord... lit ends". Pow, there's the smoking gun, I bet. Something told me that was screwing me up. Right after work I replaced the cable with a regular 16ga, unlit, and it worked perfectly.
Problem diagnosed just with the gentle prodding of "show me what you did"
I went with the lit ends to provide some kind of "load end" indication that power was actually flowing. I'll try reinstalling that one end tomorrow - I think the wall-end being lit may have soured the neutral, and snuck power all the way to the end of the "turned off by ssr" cable.
Thanks! I'll be installing into the project box tomorrow. Just have to find a bit of thermal compound, to mount the ssr to the box (furnace is only 500w, so shouldn't work the ssr too hard!)