I didn't check the links but your approach is interesting. I am always amazed when anyone "believes" a theory of the universe at or near 100%, often based on "no more plausible explanation". I remember Martin Rees claiming he had moved from 90% towards 99%+ certainty in the Big Bang Model. (I think it was in his book "Just Six Numbers" published in 2001). Regardless of the level of consistency with what we have observed in the past few hundred years it seems to huge an extrapolation to have that degree of "faith" in it, though I suspect it is mostly based on the weakness of the alternatives.
The Cyclic Universe is an extended extrapolation of the Big Bang Model in some presumably Sinusoidal form (I think?)
Personally I "prefer" a steady state model from a philosophical point of view, though it would require a different set of assumptions from those that presently disfavour it, including further rewriting of the second law of thermodynamics than that needed for the Cyclic Universe (as Insane Alien pointed out).
Can't say I "believe" any theory in particular, but find it very interesting what "odds" others, scientists or armchair scientists such as myself, would give each theory. It would be interesting to see some well thought out polls on this.