I finally got around to having another go at cleaning my sensor. I think I'll leave well enough alone at this point. The current condition seems much improved. I see three obvious spots, and I feel comfortable ignoring them since they do not show up in "normal" (i.e., non-dust-detecting) photographs, whether the images are processed or unprocessed. Only though choosing deliberately close levels in Photoshop to look for/find/show dust do these three spots appear. This will do for now. It happens to be that the sensor is now cleaner than it was when the camera was new. That helps take the sting out of the frustration of a few days ago.
To give more information on the cleaning, I cleaned the sensor today with a Visibledust VSwab (green) moistened with VDust Plus. After taking a test shot, the smears and fibers of before were gone, though there remained a section of droplets on the right side of the image--something along the lines of what an inefficient wiper blade might leave on your windshield (windscreen).
I then wiped the sensor with a second swab moistened with Visible Dust's Sensor Clean, and that got me to what you see in the attached image. Before and after each swabbing, a Giottos Rocket Air Blower was used, and I insepcted the sensor with a VisibleDust Quasar Sensor Loupe 7x.
In the past, I was able to get a T3i Rebel sensor cleaner than what you see here, and it was when shooting the test image at f/32. Only one faint spot would show up in the photo.
For the images I've posted, I photographed an overcast daytime sky. Part of my interest in having dust-free images at f/16 is because I photograph aircraft from time to time, and the shots are taken often in the f/10 to f/16 range. With the sky as a background, dust spots are easily seen, and when there are upwards of 17 of them (which was the case with the then new T3i), removing them in post is can be a "PITA".
Practice and proper technique are important in sensor cleaning. As VisibleDust cleaning swabs are somewhat expensive (over US $40 for 12 of the green 1.0x size), there is incentive learning good technique quickly. In the meantime, I am waiting for delivery of a Lenspen SensorKlear II so that I have another option for future cleanings.
I give my sincere thanks to those who replied with their helpful comments and suggestions. I also stand with Neuro in his caution against doing more than is warranted under given contexts or circumstances.