I'm sure you've been waiting with intense anticipation for the outcome of this saga. Well, wait no more.
I have to admit here, that I did not adhere to Jim's troubleshooting method. (It takes a great effort to pull my compressor from the barn and haul it over to the equipment shed. That said, I thought long and hard again about the symptoms. It had to be fuel starvation! It would run 27 seconds at full throttle, and about 33 seconds at an idle. Not knowing the rate of fuel consumption, I convinced myself that this must be the amount of fuel in the bowl, and that it was not being replenished by a sticking needle valve. I bought the valve ($18), and a little O-ring ($1) that I may have messed up with my multiple dis-assembly/ assembly activities.
I put it all back together and it started right up (as normal). It ran for 27 seconds and died (as the new normal). I could see there was fuel in the filter. I tried to re-start it immediately and there was a tremendous backfire from the exhaust. I was glad there was nothing flammable nearby, and my hearing came back within a few minutes. This told me there was too much fuel, and not enough spark?
Out of shear desperation now I installed the $2 spark plug I had previously bought. (I didn't install it before this time as the symptoms did not fit.) The mower started right up (as normal). I realized I had counted to 53 seconds when my brain said, 'hey, dummy. That's longer than before.' 2 hours, and the side and front yard later, I put it away in the shed.
I don't know why I make my life more complicated than it really has to be. Yet another reminder to always try the simplest, and least expensive, things first. GreenRules and Midniteoyl rule this thread. Thanks to everyone's assistance!