I think that is probably the reason that Ashtekar, who is longterm friends with Penrose and must have heard Penrose talk about entropy and bounce on countless occasions, has never seemed worried by Penrose's thermo objection. Admittedly this is not spelled out rigorously, but it's in the context of a novel situation and I find that, to me, intuitively it makes sense.
I have always thought it intuitive that gravity was driving entropy (and time itself really). It is very interesting to see this pointed out with respect to Ashtekar's perspective, especially the sign reversal for entropy itself when gravity's sign changes.
It also seemed to me that a bounce would "fix" entropy so I have favored that idea over a pure big bang. It certainly answers the question of why the universe got to be so ordered. It will be interesting to see if this idea holds up under observations over the next decade or so.