Just remove the likelihood statement from your model, and then you will sample from the Jeffrey’s prior! If you want to be fancy, you add an if statement around your likelihood statement, and provide an additional integer data input “LL” (or named similar) that is allowed to be 0 or 1, and let that determine whether you calculate the likelihood or not.
The join posterior distribution of shape and scale of a gamma distribution should always be expected to show a lot of correlation. This is because infinitely multiple combinations of of shape and scale produce the same mean (because of the multiplicativeness). This has little to do with the priors that you specify for shape and scale. My suggestion is to reparameterise the model in terms of mean and shape, so to change the parameters that you estimate. Mean determines the location of the gamma distribution, and shape determines the variance relative to the mean. Therefore, mean and shape usually aren’t very correlated in the posterior (regardless of prior definition).