Hi Pierre,
Your length of wire (9.38m) is very close to the half-wavelength on 14MHz. This will present a very high impedance at the feed-point which is a problem for any tuner. Even if it can be matched do not expect a very efficient system.
When you shorten the wire to 7.50m you are now very close to the half-wavelength on 15 and 17m resulting in the same problem, but now on different bands.
In general you should avoid tuning a wire close to a half-wavelength (or a multiple thereof) with a built-in antenna matching network.
Alternatives would be to use the original 9.38m and use either a step-up transformer (currently discussed in a parallel thread (Toroid windings for EFHW) on 20m or a quarterwave length parallel wire tuning stub converting the design into a J-pole. For all other bands you could use your KX2 with tuner.
Another alternative would be to use the shorter 7.50m wire on all bands except 15 and 17m and use an additional clip-on wire for these bands. Again avoid going near half wave on any operating frequency.
73 Heinz