I'm of two minds here with a reluctant gut feeling.
On the one hand, there are actual problems with inflation theory, from the extremely low probability of the event even taking place at a 'time' before what we understand as time even existed, to the fact there are a couple of ways to define multiverse/distinct universe that smear the bounds of discussion. On the other hand, even the paper they referenced fiddles with values of a bunch of parameters and notes one of the defining, fundamental factors as changing so slowly it's effectively constant on cosmological timescales. I can't even hazard a guess at what could be a test for this model's remnants in the universe's structure. It also overhauls dark energy, but now as a necessary condition for the bounce to occur, which I can't easily explain or infer.
That said, as someone who only dipped his toe in the subject, I can see it as promising, but a long way from rising up to the proclaimed:
“You know it works when you don’t have to ask under what condition it works.”
EDIT: Undeleting unchanged post after reading a bit further and, broadly, not changing opinion.