Hi Rémy,
Thanks for posting your variable transformer solution!
Concerning the transformer, I came to a similar conclusion. I didn’t measure the antenna impedance directly, but the impedance and SWR on the transformer input side.
To measure the influence of the HF bands in relation to the transformer ratios and shunt capacitor, I built a special test coupler.
In my Portable 7-Band EFHW document on page 32 and 33 you can see different SWR curves for each transformer ratio (1:36, 1:49, 1:64 and 1:81), measured three times with different shunt capacitors (0, 82 and 120 pF).
Following, as an example, the measurements with a 82 pF shunt capacitor:
Apart from ground conductivity, height above ground, antenna configuration and wire diameter, the impedance seemed also frequency dependant, i.e. it is higher on lower frequencies and lower on higher frequencies.
73 Stephan