What you have described is how Doppler radar works, an application of the Doppler effect, not the Doppler effect itself. Absorption and emission are not required. The Doppler effect is the change in frequency of a wave in relation to an observer moving relative to the wave source. Cosmological redshift looks like the Doppler effect, but it's not. It's due to the expansion of space, not the motion of an individual body.
The "Doppler Effect", as you've described, is an observation with causes as diverse as the waves. The Doppler Effect with electromagnetic waves is a result of a receiver not being calibrated. Once calibrated, Doppler Radar is possibly by measuring the frequency change of re-emitted energy (there's no such thing as reflecting as a change in energy will always occur). Eliminating re-emittance is the basis of stealth. With photons, re-emittance is required for any frequency change to occur -or- your device hasn't been calibrated and is giving false readings.
What you are saying here has no relation to reality. There is a difference between absorption and re-emission (such as what happens in fluorescence, or emission of black body radiation (also 2 different things)) and reflected light. Go look up those terms online if you don't know what they mean.
You apparently haven't bothered to even read the Wikipedia page on the Doppler effect I linked before, which clearly shows it applies outside the context of radar, and it typically refers to a transmitter and receiver moving at different velocities relative to each other, with no need for any signal returning to the original transmitter to be discussed.
No re-emission is needed for there to be a Doppler shift. Paint an object black and you can still measure the effect as the difference between the energy and momentum from the frame of the source to the energy and momentum imparted to the receiver in its own frame.
How the heck does "painting something black", assuming it will then absorb all light, become a means to measure a photonic Doppler Effect? And if it "can still be measured", assuming with radar, what was the point of painting it. What are you inferring or attempting to talk about?
Radar has nothing to do with what I said. You measure the effect, because you are holding the piece of material and you can measure how much energy it received from the incident radiation and how much momentum was transferred to it. This is the basis of how cameras (or your eyes) work. If a camera is moving towards a light source outputting a fixed frequency, it will detect higher frequency light. If it is moving away it detects lower frequency light. No discussion of radar, or re-emission, or reflection is required. (And you know the frequency of the emitted light in the rest frame of the source, because you use something well known and fundamental, such as the emission spectra of specific elements.)
1) As this thread suggests "New Physics" to explain all conventional theories to date being incapable of describing the Universe, I would suggest correcting the use of existing theories rather than make up fantastic energies or matter to fill the void of ignorance. All science starts with "I don't know", but if that is replaced with mythical, unmeasurable "things" - it's not really science.
You should correct your own understanding of physics before you try and claim that you understand astronomy better than the people who have devoted their lives to it. Attaching a label to an area of physics that is a "known unknown" is simply a tool to facilitate discussion. Your continued attempts to make fun of scientists are still inappropriate, especially since it is for wanting to not have to say the mouthful "that thing where the universe has accelerating expansion and we aren't sure why" thirty times per conversation. Scientists have given it a name to facilitate discussion, and quantified the correction factor needed to make existing theories match the data. There is nothing mythical about it, the data they measure is real, and it is no secret that the reason for the discrepancy between unmodified theory and measured data is not understood.
2) I would suggest avoiding the crutch of theoretical mathematics. Math is a language with rules. But one can just as easily assemble a meaningless word-soup (as mentioned above) as assemble a meaningless equation of jibberish.
What you appear to be saying here is that you don't understand math and won't be bothered to try. Math as a language is a whole lot more rigorous than English, and if you know what you are doing can be used to prove things and communicate with others. If you form gibberish in it, there is also a way to show that it is gibberish.
This disparity between reality and mathematics doesn't just occur in astronomy, but also subatomic particle physics (often ridiculously renamed "Quantum") and complex systems like fluid dynamics.
Quantum has a specific meaning, which relates to the quanitzation of physical properties at the level of subatomic particles. Since this is the usually the most important feature of the behavior of particles at the subatomic level, I fail to see how it is "ridiculous" to name the field after the category of effects that dominate it.
I have no idea what your issue is with fluid mechanics, as fluid mechanics equations work despite the complexity (the equations contain the complexity as well, which does make them usually unsolvable in simple closed forms), but you have drifted completely off topic here anyway.