Hello, I don’t have an answer to your specific question. But I would suggest you to consider the Generalized F distribution, which in theory nests the Generalized Gamma, but actually easier to work with. I also learned about it from the flexsurv package. I shared my stan code: Generalized F distribution can reduce to Generalized Gamma distribution - but what prior to use? - #2 by Bob_Carpenter
I hope this is useful in some way.