Barbero-Irmizi and LQG observables?

• A
Iliody
TL;DR Summary
Do actual LQG formulations depend on Barbero-Immirzi parameter, or they are independent of it?
Hello, around 2008-2009 I self-studied a little bit of LQG, and become disillusioned by it because I understood that Barbero-Immirzi parameter was related to time parametrization (in a way similar to a scale factor, like $c$), and the dependence of observable mean values was in conflict with General Covariance, at least as I understood it. The last year, I was reading things about CQFT that talked about Group Field Theories, and they looked really well, even if they hadn't reached a limit with four-manifolds like how our macroscopic spacetime looks. Because GFT appear to be related to LQG, I suppose that it had become better. A guy told that made his MS thesis on LQG told me that today Barbero-Immirzi dependence on LQG was overcome. Is that true? Are there any paper that you would recommend?