Binomial with over 700 parameters to be estimated

There is visible bimodality in qlogis(theta[1]). One thing to consider is, whether values qlogis(theta[1]))<-10 are sensible. I suspect that this the region causing part of the challenge. Even if it would not be sensible prior, you could check if qlogis(theta[1]))<-10 region is problematic by adding a prior making those values very unlikely and then you could see if the sampling is more efficient in the region of larger qlogis(theta[1])) values.