After pulling my hair out trying to figure out how to make sure my electronic first shutter curtain was up and out of the way combined with Mirror up mode I finally figured out a way to get it. I control the T3i from the computer using EOS utility. I set the mirror up to enable. I set the Drive Mode to a timer delay of 2 seconds. I like to use StackShots Auto-Step mode. I have enough T-Settle time and Pluse times to where I'm about 6 seconds between shots.
If I didn't use the 2 second timer delay I was getting vibration from shutter movement whether using stack shot or EOS utility's shutter button. And when you exit Live View to let stack shot take over (without the timer delay) I would still see degraded resolution with my test shots. Each shot though was with Mirror up enabled, I didn't try disabling MU on any shots.
When I magnified my raw images shot in Light Room I could clearly see the difference between MU only and MU + 2 second timer delay. As Charles said EFSC is out of the way by default in Live View. The 2 second timer delay seemed be the only way to trick the camera into thinking it is shooting in Live View mode shooting with the first shutter curtain up and not moving.
Here are the 2 shots. They aren't stacked, it was shot at 4x with the MP-E 65mm, 1/40 sec, ISO 200, LED continous lighting, Manual mode, Auto WB. This is a tiny chip of sand where each grain is about 1/20th to 1/50th of a millimeter, tiny stuff. At this point I'm not concerned about anything other than resolution improvement. The first shot is much sharper when magnified to 200%, you can't really see here very well. Plus I shrunk these jepgs down from 10MB to 100KB to upload.

