I have a hard time understanding you. Why do you say "the universe in the first 13.7 billion years don't like to exceed this speed". I have a feeling that you are mixing up two different kinds of velocity. Try reading,
Cosmology Tutorial - Part 2
I'm according with you, but:
Hubble's law relations distance-speed and also time (distance with time).
So if the radiation of cosmic microwave background go before more quickly that c, later need to brake, if brake means:
the the radiation of cosmic microwave background may to see at the average speed but for example if before the 1/2 time of the universe has slow the speed, the stars at 1/2 distance would see at 1/2 of distance but at real speed. (same if ti was at 1/4, 3/4, ...) - the light that we see of stars at 1/2 of distance is also at 1/2 of time.
If this occurs the Hubble's law would be false, because the relation distance-speed don't concordate.
So, to be according to Hubble's law (it's a law), the speed need to be constant, and how in a expansion threre is not real speed this is equivalent to a constant speed and by that the expansion is decreasing (a expansion to maintain a equivalent constant speed each unit of space need to expand decreasing).
Thanks by your note.
Please, say me errors of my note.