For example: last night, I briefly considered the 'Multiple Interacting Worlds' interpretation of quantum physics, in which it is postulated that there are a large number of universes, each of which has pure Newtonian physics internally, but whose interactions with near-identical universes cause what we observe as quantum phenomena. It's very similar to the 'Multiple Worlds' interpretation, except instead of new universes branching from old ones at every moment in an ever-spreading bush, all the branches branched out at the Big Bang.

The "Many worlds" interpretation does not postulate a large number of universes. It only postulates:

1) The world is described by a quantum state, which is an element of a kind of vector space known as Hilbert space. 2) The quantum state evolves through time in accordance with the Schrödinger equation, with some particular Hamiltonian.

That's it. Take the old Copenhagen interpretation and remove all ideas about 'collapsing the wave function'.

The 'many worlds' appear when you do the math, they are derived from these postulates.

http://www.preposterousuniverse.com/blog/2015/02/19/the-wrong-objections-to-the-many-worlds-interpretation-of-quantum-mechanics/

Regarding the difference between 'the worlds all appear at the big bang' versus 'the worlds are always appearing', what would the difference between these be in terms of the actual mathematical equations?

The 'new worlds appearing all the time' in MWH is a consequence of the quantum state evolving through time in accordance with the Schrödinger equation.

All of that said, I don't mean to criticize your post or anything, I thought it was great technobabble! I just have no idea how it would translate into actual theories. :)