So, which experiments cannot be explained in any way other than invoking SRT? We begin with some subsidiary remarks. We shall not discuss in detail the issues of quantum electrodynamics, because its predictive accuracy depends only slightly on the accuracy: (this is with motion of the receiver; and light speed can be constant with motion of the source, for example, by analogy with the sound speed), but nobody even made an attempt to consider light speed to be not a constant.
The stellar aberration phenomenon is fairly explained by the classical physics
 and is determined by the following two principal facts:
(1) by changes (throughout an year) of the velocity of the observation system, basically by the orbital rotation of the Earth (this absolute state does not depend on the rectilinear motion of inertial systems and on the presence of ether or medium), and
(2) by the rectilinear propagation of light beams between the source and the receiver for inertial systems (it is a result of the light particle inertia for the corpuscular theory, or it is a result of Huygens' principle for the wave theory).
Recall once again that upon "entrance" into our measuring device the light has
fixed direction and frequency (the prehistory of the process is not so
important: is it the motion of a source, of a "medium", of a receiver), and it
is this "particular light", with which all measurements are carried out.
The Fizeau experiment is not critical, since it allows to write light speed
in a medium as
and the measurement were carried out for a particular fixed frequency , i.e. and have not been compared, which is impossible to be done in the Fizeau experiment.
The attraction of a lifetime of muons for proving the SRT is a pure speculation. The modern mankind cannot create two inertial systems moving relative each other with relativistic velocities. And it is not worth to mask quite a different reality in imitation of the claimed "experiment". The lifetime of unstable particles must depend on the conditions of their formation (even a stable nucleus can become excited or unstable, or, on the opposite, the recombination can take place, etc.), and the conditions of formation of muons at the altitude of upon collision of high-energy cosmic rays with nitrogen or oxygen atoms differ from the conditions of their formation and confinement in the laboratory. To say nothing of the fact that even velocities of muons, their accelerations and intensities of flows do not determined at different altitudes. Measurements, which made in accelerators, most likely testify to influence of accelerations and fields on the concrete decay process of the concrete particles. The "muon proof" was appeared in all SRT-textbooks starting from 1935, but some later it was be discovered that 1) muons origin at any altitudes, and 2) their penetrating ability considerably increases with enhancement of energy. But the relativistic pseudo-proof was not be excluded from textbooks for students (to the question on scientific ethics).