Try doing MFA with your 24-105 on your 5D3.
My first MFA efforts were done at 30 feet for my 4 L lenses. Unfortunately, much of my photography is at 50 to 100 feet, sometimes greater. So, using a 'ruler' type MFA target at 75 feet or so, my images went from 'just a tad soft' to noticably sharp. Even wide open, ISO 10,000 at 1/200th at night gives stunning results. It's right up there with the 24-70 f2.8L mark i I used to own as far as IQ in my opinion. Don't forget that the 5D3 has separate MFA settings for wide and telephoto for zoom lenses.