No. There is a reason for why Einstein and physicists have the upwardly accelerating elevator and rocket analogies. It's because experimental evidence shows that gravity behaves as if the Earth were accelerating upwards. These experiments are why Newton's theory of objects falling down through space to the earth was rejected. Gravity operates as if the Earth is accelerating upwards, and this is reflected in the equivalence principle experiments.
As @AllAroundTheWorld mentioned, this only applies at a local level, and the key word is “as if” the Earth is accelerating upwards. It all just depends on the frame of reference. To Isaac Newton sat on the ground, it looked like the apple was falling from the tree towards the Earth. To the apple, it will have felt like the Earth was rising up towards. It doesn’t mean that the Earth is actually accelerating upwards, just feels it is, but its impossible to differentiate without further experimentation. That he did, at a micro and macro scale, and came up with the theories we now call Classical Mechanics.
With his observation, deduction, and verification through experimentation, Newton was able to come up with models for motion and gravitation that accurately predict the motion and position of not only things on Earth like projectiles, but astronomical bodies in orbit around each other. No such testable model or theory exists under FET, just an ascertain that because the observation is like the Earth is constantly accelerating upwards at 9.81 m/s, it must therefore be the case.
As time went on, and understanding increased, the phenomenon we call gravity was explained by curved space, which is a completely equivalent principle. Under this model, gravity is not a force, it’s a geodesic through space, and only felt if one deviates away from that geodesic. The following recent (at the time of writing) is an interesting presentation of the principles:
But, let’s assume that under FET, the Earth is accelerating upwards. Under FET, that also means that everything we see above us is also moving upwards with the same acceleration, including the planets, stars and galaxies, right? If this is the case, why are the effects of gravity different on different sized planets? The planets are used to help slingshot probes into outer reaches of space, and so the acceleration due to gravity is well known. Or are such launches just faked, there are no probes and the photos are all made up? That’s not a condescending question, it’s a probing one (no pun intended).
In your post you also make reference to the effect of redshift and blueshift, which means you must accept the phenomenon, right? Objects moving away from us exhibit redshift and vice versa. Experimental observation of thousands of galaxies shows that they are all exhibiting redshift, indicating they are all moving away from us, and at a rate of around 67 km/s/Mpc. Stars in our local galaxy also exhibit redshift and blueshift.
Assuming FET is true and the stars and galaxies are just points of light in the dome, it would mean that something is slowly changing the colour of those lights. Who or what is controlling the colour of those lights? If they are close in a layer above the Sun and Moon, it all seems like a bit of an extraordinary effort to individually control the colour of thousands/millions of different objects to give the impression that the distance to them is changing.