No, that is fine, -- I honestly don't remember how non-constant acceleration is treated in relativity, but I can look into it later.
For now, do you or do you not dispute that the nature can be viewed and its laws understood, albeit with a different amount of effort, form any reference frame, even a variably accelerated one?
Science going back to the Greeks was based on an assumption: that the laws you observe on earth are universal and apply everywhere in the universe. That hasn't change with modern physics.
By the way, I read someplace recently that some physicists think they have detected the graviton for the first time. This would be a confirmation of the prediction of quantum physics. But quantum physics and Einstein's theory of relativity contradict each other and both cannot be true. It will be interesting to see if anyone can duplicate the results, or if this is just some fluke in the data.