You can try timing the two options as I mentioned above. One using value as an argument on the call signature but not using it and instead embedding the data in the loglik function and another using the value argument. I don’t know enough about the internals to guess if there will be a difference or what that would be.
The warning about the embedded data approach I wrote above is because you might run into shape issues, but if you only sample the model on your data and don’t try to resample on different data or generate posterior predictive samples I think everything should be fine.