Managed to make it by doing a little like you said, however with a little change !
The 2 Wisplash weren't powerful enough to reach Mach 1.5 at 15km altitude, I had to use the 4 engines at the same time to get an 70km apoapsis. A lot of fuel has been lost because of this, but I'm now in ~100km orbit, with 1500ms (Dv) left. I can now go on Minmus again ( finally ), but probably not travel back to Kerbin. I guess it's all about optimization now !
Quickly after being in stable orbit, I tried your method (partially combined with Foxster's one, about the 10° climb). Max speed of ~1250km/h at 20km altitude, did a slow climb trying to get at 40km altitude and lost ALL my vertical speed. By burning fuel for a long time, it has lost a lot of mass, and I finally got an ~70km orbit, but with only 800ms left
I don't know why it does that, I tried it both times and sadly it didnt worked as expected.
Thanks anyway !
GEEZ ! I made my flight path a little like you : 20°degrees until 6500m (what you did), then I aimed at 30° and at 10km altitude, I turned on LV-N engines : With an ~100km orbit, over 2000Ms (Dv) left ! WAY, WAY better than what I ever expected to get. Almost the half of the fuel unused too, and there wasn't any optimzation at all !
Thanks a lot all three of you, I can sleep in peace now !