Unfortunately, I can’t really dig deeply in the model due to time constraints. There is a bunch of diagnostic techniques briefly mentioned at Divergent transitions - a primer, which could help you investigate further and gain some understanding. I would definitely try to simplify the model further to see when the problematic behaviour disappears.
I might be misunderstanding you here, but it seems you are conflating a correlation in the model (e.g. when two parameters are modelled as multivariate normal distrubted) and a correlation in the posterior, which can happen regardless of whethere the model (or more broadly the data generating process) has any correlations. I.e. you can easily have all sorts of weird structure (including correlations) in your posterior samples, even if your code to simulate the data perfectly matches the model and there are no correlations in the model. Understanding why this structure arises in the posterior is often the best way to diagnose and resolve issues - unfortunately there is no general way to do this, one needs to think hard about the model one sees.
Best of luck with the model!