That's why I started this thread. The behavior of the lens is erratic.
I started with this lens at IMG_7584 and finished with IMG_7886. 3 hundred photos, over two hundred of which under bench testing conditions (literally... my kitchen bench... :rolleyes
. Hardly trade show experience... 
I have a PhD in Engineering and just about 30 years of experience, most of it spent in research testing. Nothing to do with optics and cameras, although my PhD thesis was in non-linear wave diffraction (water waves, not light waves which are easier to deal with)... What I am trying to say is that I have enough testing experience to be able to judge the efficacy of the target/method and the variability of the results.
I have done 2 series of tests with the same test matrix I discussed in my original post. The first one was with Live View, the second one with viewfinder targeting/AF.
In my experience, when shooting handheld, I achieve better results with AI Servo, however, for tripod mounted camera shooting, I think I would increase the chances of inducing BBF camera vibrations than I would gain from AI Servo 'accuracy'. So One-Shot it was...
A priori, the Live View photos displayed as much or more variation. I attributed this to the fact that manually focusing until confirmation was not accurate enough (when you hear the beep you don't stop instantly). So midway I stopped MF and went to Live View AF... Just as bad... That's why I went to VF/AF.
It is difficult to describe the whole spreadsheet, but basically there was no monotonic increase (or decrease) with FL or distance. Since I used only three apertures, I just noticed the variability with no further comment.
My take is that this is a very complex lens (13 groups/18 elements), so if one or more elements are out of tolerance, the variations are pushed all over the place, as these elements interact with the others. Of course, my EF 70-200 MkII is even more complex (19 groups/23 elements) and it nails it every time...
The clincher for me was that at near infinity (20+ feet) it front focused, making infinity soft... I don't have MFA in my super Rebel and I did not want to get stuck with a lens which Canon might have problems adjusting.
Had the lens displayed a less complex behavior, say front focusing progressively as the distance decreased and no other variability, I would probably keep the lens and take my chances with Canon service.
Thank you all for your interest, I will keep you informed.
EDIT: One last thought... if the erratic lens behavior is due to 'delicate' (rather than 'robust') design, this may be the reason for not having IS. Adding another optical group might be too much to take...