Adey,
I thought I would give your mission a go today. Two fresh thought into the melting pot.
1) When deciding a suitable distance last time, I initially tried 14 feet. Without a TC on, my Nikon 28-105 outperformed the fixed 105.

Moving to a distance of 20 feet soon sorted that one out.

The 105 is therefore happier at 20ft to infinity as at those ranges it outperforms the zoom.
2) I have used the TC for close ups with tubes and 55 micro very successfuly.
In view of the above I therefore decided that for your various aperture test to move the subject out from 20 feet to 35 feet. Composites attatched that show that at that distance the TC performance fell apart. Shed loads of CA at f4 so no point in going wider.
I did the 400 with and without, at 40 feet and the attatched are processed crops. In view of the 105 and distance experience, and as the sun is due to return next week, I will then try the 400 and TC at longer distances.
Pics attatched
1) Todays test target
2) Comparison at 20 feet and 35 feet using 105 plus converter
3) Aperture comparisons at 35 feet using 105mm and converter
4) 400mm at f5.6 at 40 feet - processed crop
5) 400mm and converter at f5.6 and 40 feet - processed crop
Don