Although I'm no expert, my understanding(from listening to others, like Stefan) is that the main charges aren't based on the PL's version FFP which were introduced as late as 2013. They seem like charges of dishonest accounting, concealment, false reporting etc. I don't think the Mancini, image rights or non-cooperation accusations come under the FFP regulations either. It's all in the regular ruleset.
There are some references to adhering to UEFA's FFP regulations though which were introduced in 2011.
The PL have to govern their regulations in accordance with English law and a 6 year limitation would normally apply. However, that is not the case for accusations of concealment, which is how they are able to go back so far.
I think the PL has already explored any time barring issues before they brought the charges and City's side has already done the same. That doesn't mean they have sufficient evidence to a comfortable satisfaction though. Also, if City do have irrefutable evidence, then even if the PL think they've got something now, they will know they don't quite quickly at the arbitration.
Hopefully anyway.
For me, my mind keeps coming back to the fact that UEFA claimed they had proven their allegations to a comfortable satisfaction in accordance with Swiss law. They seemed to have briefed the press: "There is no way we have got this wrong, our AC panel are law experts". They tried to penalise a club on that basis("we've proven it") and we only found out they were wrong/lying thanks to CAS. CAS were the ones who got slated, when it definitely should have been UEFA, that should not be forgotten either.
Having no route to a different body/court is still a concern for me, I understand these are professionals but we were told the same of the CFCB. As I alluded to above, none of those who worked on the CFCB arbitration suffered reputational damage for bringing an incorrect verdict, that I saw.
If City feel the commission isn't independent after all, or that they aren't giving the proper due process, then City are pretty much screwed. If UEFA were allowed to select another panel of arbitrators, I have no doubt they would have backed their buddies on the first verdict by default.
The independent regulator can't come soon enough if only for piece of mind. Hopefully it(no route to take it elsewhere) turns out not to be an issue at all, we'll have to wait and see.