Peter
"It's probably my fault calling his rejected 'ether' frame a 'background' frame..."
It does not matter about a correlation between what was said. The point is, as light works in a fundamental way, then if one calibrates its speed with respect to some individualistic frame on each occasion, then the same answer will result. But this is not the speed of observational light. That is a function of the duration incurred from its creation, as the result of an interaction with whatever occurred, to its receipt by anything (but it has to be a sentient organism which can indicate in some way that reception has occurred!).
"about SR from 1905"
Really? When was the first time he mentioned SR? Not that it matters because in 1916 he defined it, and it is different from what was said in 1905. Fundamentally in 1905 he has two states of existence. Light is in vacuo. Everything else is not, because there is length alteration (ie some force is operational). This is why he recognises a potential conflict between the two postulates ("apparently irreconcilable"), and is so concerned with states of inertia. One cannot have a theory where two different 'elements' are in different states of 'being'. So as far as he was concerned, SR resolved this. In SR there is no force at all, in GR there is.
And it is not what he said, intended to do, or thought he did, that matters. That is what he actually did. And he failed to understand how timing worked (which resulted in a superfluous layer thereof) and conflated reality and the light reality (which resulted in him losing a layer of timing). The nearest he got to acknowledging a differentiation was when speaking of "immediate proximity", when he said the times would be the same, which they are not. He can speak of frames of reference , observers, etc, but they do not exist if there is no observational light. Nobody receives that ray of light, and I would certainly not sugget trying to see with lightening!
The point being that this holy grail of trying to resolve rate of change and light speed does not exist, because he never had any light in the first place. All he does is use a constant to calibrate duration and distance. And it happens to be the speed of light. Obviously, he and all the interpretations since, believe this accounts for observation, but it does not. In effect, the difference in the timing of the receipt of light has been shifted to a characteristic of reality itself. This is his best statement on the nature of relativity (forget SR, that is a red herring):
Einstein para 4 section 9 1916
"Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event. Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, ie that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in section 7) disappears".
This is rubbish. Events are events, they occur at a time, and at one time only. They do not occur wrt some other event. What does happen is that the timing of receipt of light varies depending on spatial relationships, and if there is relative movement then the apparent rate of change will appear to alter for the recipient from that which occurs.
Paul