No cyclical model can avoid a thermal equilibrium fate unless energy gets added to the system.
I agree with you that even cyclical models can’t avoid a starting position.
Sorry, but I'm not quite sure what you're saying here. It is possible to evade the BGV theorem with an oscillatory/cyclic model that globally on average has an expansion rate equal to zero, though the latter, of course, is still conceptually absurd; but, then, in order to evade the singularities left in the wake of the contraction phase, the arrows of time must be reversed at
t = 0 as in Aguirre-Gratton (2001). This constitutes a thermodynamic beginning!. It's unavoidable. A cyclic model that globally an average has an expansion rate greater than zero cannot be past-eternal either, even though it can, theoretically, cycle into the future forever once it gets started. The fundamental issue with cyclic models is the Second Law of Thermodynamics, which essentially states that entropy continuously increases in closed systems. To avoid heat death, the universe must get bigger and bigger in each cycle so that the amount of entropy per volume doesn't increase, but this means that the universe, as extrapolated backwards, was smaller and smaller in each cycle—converging to a point of zero volume and time, i.e., the very beginning that the cosmologists of cyclic models are trying to avoid. Either way, either the generalized principle of thermodynamics or the standard principle of thermodynamics stands and stays, and cyclic models, as you say, must have "a starting point."