Stefan
your idea of saturating the transformer is, I think, flawed.
If you reduce mu-r of the core by saturating with DC, the primary
winding will have vastly reduced inductance and appear as a near short
circuit to the transmitter - not what you want
The idea of saturable reactors applies to resonant inductors,
where you use the DC to change the inductance. So it could be
applied to a class D transmitter with a tank arrangement, to retune the
tank circuit to adjust for match, or control amplitude.
Andy G4JNT