The frame of reference is irrelevant.
Incorrect. The frame of reference is absolutely crucial. If you believe it to be irrelevant, simply choose your favourite one. I'll give you a hint, there are three FoR's that are worth considering here: a local observer standing atop the Earth, a local observer located immediately above the Earth who is initally at rest relative to the Earth, and an external inertial observer.
If I'm accelerated in a direction and nothing is stopping me, I will acquire speed.
Correct, but entirely irrelevant. The magnitude of that speed is the key point here, not the fact that it's increasing. Specifically, your claim that "the flat surface we would be on is now travelling upwards at quite a fast speed
(incredibly greater than the speed of light)" contradicts basic physics. You cannot identify a frame of reference in which the Earth is moving faster than c without contradicting Special Relativity. As was the case previously, I suggest that throwing physics out the window is not the best way for you to defend RET.
because you're not in a different system S' but you are on S
If you're
on S, your speed relative to S is 0m/s, and the speed of S relative to you is 0m/s. That's significantly lower than c.
Its not messy, I'm talking about redshift/blueshift for uniform acceleration which is part of EP and is used as evidence to back UA.
So, here's the thing. I raised specific objections to what you're saying. Responding with nothing other than "it's not messy" is not going to cut it.
For example, if we have a rocket accelerating at 1g away from any gravitational field with two observers onboard
This is where you fail. The Doppler Effect is experienced when two bodies are in motion
relative to one another. I already explained this to you, but you chose to ignore it. Two bodies accelerating upwards at the same rate and with no initial velocity will be stationary relative to one another. Thus, UA itself is not going to have any impact on the Doppler Effect.
The light from the stars directly above the Earth would be blueshifted and an observer on one of those stars would see the Earth being redshifted.
This would be true if the stars were accelerating away from the Earth. As far as UA is concerned, they're not.