"...OK for inflation to violate the light barrier because it has been decided that otherwise it couldn't have happened."
Like I said befor,e the light barrier only applies to things that have mass and energy and substance. Space and time are not "things" in this sense, and so there is no restriction on their speed. Two analogies earlier in this thread, one from Old Geezer explaining about how shadows can move at any speed, and one from my about waves hitting a beach, demonstrate that it is, in fact, easy to find scenarios in which things appear to be breaking the light barrier. In both cases those things are just points of reference, though, and so relativity is not violated at all, and nothing has broken down, nor is there any sort of cheat.
Spacetime is the ultimate "point of reference". It's just how you define where things are, and when they are there. There is no substance to it, really. And if there is no substance, there is no barrier, and if there is no barrier, there is no problem.
The phenomenon is, properly, known as "metric expansion", and the idea is firmly established in the Scientific field. It is, perhaps, one of the toughest subjects to communicate, not least because it's one of the toughest subjects to understand properly. Nevertheless, that there are in fact several easy scenarios in which you could cause some point of reference to move as an arbitrarily fast speed shows you that the idea of Inflation itself is absolutely not a cheat way. Relativity (in this case General Relativity) applies to it too, just as much as it does to anything else.
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In terms of your other question:
"[I still think that the CMB] comes from beyond our universe. Is there any way it can be proved to have not?"
The answer to that is probably something closer to "it depends". I may have noted, either in this thread or the other one about Inflation that I posted myself, that there have been attempts to test the idea that our Universe is smaller than it's "observed" to be. This could emerge from models in which you imagine the Universe, say, to be sort of a cube, with the faces acting perhaps as some sort of mirror. These are bizarre ideas, to say the least, but it is possible to go from the idea to some sort of prediction of the pattern it would create in the CMB. Essentially, you should see that the pattern repeats in some way, so that you see the same image in two or more separate points in the sky. So far, this has not been observed despite the searching.
There are two main caveats, though, to this being taken to rule the idea out. Firstly, you have to be able to go from some sort of conceptual idea to some sort of physical prediction that can be tested against the results, and this is not at all easy. And secondly, as you can perhaps just about imagine, the prediction made is highly dependent on the initial assumptions on the shape of the Universe, so that those shapes that have not been tested haven't been ruled out, either.
This can be applied to your idea too. It could be ruled out (to within experimental constraints, at least) if there were some way to turn the sketch into a prediction. This, though, would probably not be easy, and would probably not be definitive either because presumably there are many ways in which you could turn the idea into maths. Each individual idea could be ruled out, but the concept as a whole might never be. And that's even supposing that anyone bothers to try, which isn't guaranteed either, what with the success of the current model to describe what is going on. The accuracy of the fit of model to data is superb.