Yours truly has to hand it to you that after so many failed attempts
at fudging the mathematics you have finally cooked up something that
yours truly cannot refute. One good recipe among thousands of failure
should indeed qualify you are as a great alchemist in which Einstein
the nitwit, the plagiarist, and the liar did not even achieve. So,
salute to you.

The derivation shows correctly the invariance in the wavelength under
non-relativistic condition as expected. However, the transformation
of wavelength is not expected to be in the relativistic condition
according to the FitzGerald-Lorentz length contraction. So, don’t get
that over to your head too much. Yours truly now realizes that SR can
indeed reconcile with the Doppler effect all thanks to you. That does
not mean SR is flawless. The biggest flaw of SR is still the
manifestation of the twin’s paradox. So until then, we shall meet
again in the battle fields. The twin’s paradox is not something you
can cook up mathemagics to resolve with easily. So, until then, take
care.