I think you've hit the nail on the head in that the assumptions about the CMB are utterly dependant on a "singularity big bang" event being the beginning of the universe.
I suspect a universal origin something more akin to an incredibly large object shedding mass at a rate correlated with its mass could 'square the circle'.
Perhaps a means by which "ultramassive" black holes leak particles/energy at an exponentially increasing rate based on their size, almost an opposite to Hawking radiation. You'd get a big initial pressure wave, followed by a decreasingly powerful 'fart' effect, and be left with still a supermassive black hole at the center of the universe...
Biting the hand that feeds IT
