Awesome article. I suffer similarly to you in that I tend to overthink things. The best IQ test I ever took was proctored and you were given a chance to justify your answers.
My overthinking (very similar to your "lamp" problem) works for me but generated many "wrong" answers, and more importantly slowed me down (just as you threw your hands up in surrender).
That test, given to me early (maybe because I'm male) was the difference in 30 IQ points (that is SIGNIFICANT) when I explained my answers.
On another note, our eldest child was demonstrably gifted, as was our middle.
Our youngest? Not scholastically, at least. My wife worked with the school district to create a program which put "normal" kids through the gifted program.
I worked wonders. You get what you expect.