I’m not sure this model is going to be identified in a nice way. I think you’ll be resigned to diffuse estimates and/or adding external information with other data or strong priors. There are many ways the parameters can explain this data. For example, multiplying two unknowns, if one of the parameters is increased the other should decrease, but which one? Either can move and both are consistent with this model! Take a deeper look at the parameters. There may be strong correlation and some multimodality, indicating different modes which equally explain the data.