I would call it a day and simply state that those parameters may or may have not converged ,given that the marginal likelihoods are similar and your results look also rather similar between the two runs, a longer run will not change the results (for mode and credibility set), It seems that your data is highly variable given the relatively high values for two of the thetas, if you think that site rate variation may be an issue you could run a short testrun by using a F84 + G as the mutation model (but you will need to get the alpha parameter of the Gamma distribution from somewhere else).
It seems that your 9 parameter model is on the upper limit for your data given that some of histograms have very heavy tails and may be dominated by the prior for large values of the thetas.
peter