No, the steady-state model (the Hoyle-era model, not ancient eternal cosmologies) included expansion — Einstein had earlier proposed a static universe, but it turns out that’s not stable.
The fact that the universe has different features at different ages is a problem for continuous (non-big-bang) models. Why would e.g. radio sources be more common far away and not nearby? For a continuous/steady-state type theory, far away stuff should be the same (yes it’s older, but that doesn’t matter, since it’s steady state).
Not sure what you mean by self coherence causing “rogue wave” interference which leads to a CMB, and how exponential expansion causes perfect blackbody radiation. But a good exercise would be to play with the numbers to see how you can come up with 2.7K, and see what that suggests about e.g. the density of galaxies in the observable universe.
Also check out more modern “quasi-steady state” theories from the 90s.