Based on this my suspicion is your issues are to do with the data you are feeding in rather than the specification of priors. As a first step I would recommend calculating and comparing the means and standard deviations of the corresponding observables from each (e.g. “consumption series for US” and “consumption series for UK”).
Issues with mode-finding frequently arise from issues of scaling or trying to match demeaned data to a positive-meaned model variable. In your example above, it looks like dy has a steady state value of zero, assuming ctrend is a mean-zero exogenous stochastic process. In that case you should make sure your empiric counterpart for output growth has also been demeaned.
See remarks 13 and 10 in A Guide to Specifying Observation Equations for the Estimation of DSGE Models, which deal with the issues of forgetting the mean and scaling, respectively.
These should be simple to diagnose: the theoretic moments are calculated from the stoch_simul command and contained in “oo_.mean” and “oo_.var” respectively. If these values for your model-observables are quite different than those of your actual data, you have likely found your problem.
EDIT: You also asked
This depends on what ctrend is supposed to measure. Is it measurement error? In that case you would use your understanding of the actual data gathering process for guidance. Do you have a reason to suspect that there are systematic mistakes made in measuring the data? My sense is generally we assume measurement error shocks are mean zero. But there are cases in which a reasonable person could probably make an argument for non-zero mean shocks. For example it is well known that measuring inflation using the CPI biases the inflation rate upwards.
I will leave it to others on the forum to comment on this idea.