More iterations aren’t sufficient — the issue with divergences is that they indicate areas of parameter space which are difficult for HMC to explore. As a result, samples containing divergences can indicate biased parameter estimates, as the sampler systematically avoids areas of high curvature.
I’d try out the re-parametrization options listed above to start. If that doesn’t work, you might want to dig into model diagnostics (e.g. pairs plots, parcoord plots) to see if you can spot any degeneracies there.
It’s tough to say anything concrete without the actual model + diagnostic plots in front of me.
PS: I don’t expect it to fix all your problems, but divergences seem to be dependent on the order of the values in the Dirichlet simplex (I have no clue why this would be the case, but it’s documented e.g. here, and I’ve noticed this myself …)