So, at last - here's an update. We've had some very bad weather 'round here the last few days so I did't have any opportunity to test the lens with natural light as proposed.
First of all, thank you all for your help and your suggestions. I repeated the process outside (didn't have much time til it started raining again) with the following results:
- first of all: the results were a lot better for the 24-105 under these conditions (seems the 70-300mm didn't suffer as much from the suboptimal conditions last time)
- at the long end the lens is still not excellent, noticeably worse than the 70-300L@100mm and much worse than it is @24 to 35mm.
- at the short end the lens is quite good, even slightly better than the 70-300L
- af ist quite spot-on most of the time
After all I've read, I think this is quite how this lens is expected to perform - so I'm happy and I'll continue shooting other things than resolution targets

.
And btw: a little skin oil really helped the hood. It's still stiff and not very smooth running, but it is okay for me now.
Here is how I tested:
- Outside, ISO 100 ~1/300s-1/500s, f4
- IS off
- no filter
- Sturdy heavy tripod
- EOS-Utility attached to my laptop, LiveView with maximum magnification
- Distance to Object ~25 times the focal length to keep the target size consistent (target was about the size of the center viewfinder circle)
- Used only the very center to judge the sharpness
- MF and AF (to review the results of my afma settings obtained last time)
- focussed manually using the Liveview on the Laptop and did some Photos.
- with "AF on" I checked if I could improve things by overriding the focus manually (which hardly was the case).
- took some Photos using AF only (for comparison)
- tried to optimize the results using the AF-controls of the EOS-Utility (focus to infinity, phase AF, correct step-wise and count, repeat, feed the result back to afma)
After trying both the manual (operating the af ring by hand) and the AF+EOS-Utility (operating the AF step-wise by software) approach to afma, I think the latter is quite a bit easier/faster to do and yields very similar results.