Maybe I am missing something. GMM = generalized method of moments, correct? That is a method for fitting dynamic panel models. FMM = finite mixture method. That is a method for fitting multi-modal type data, where the response is a single value, but is generated by different processes. Not really dynamic, and definitely not suited for panel type data.
As you state, GMM is supported by PROC PANEL and PROC MODEL, but it is not supported by PROC FMM. So far as I can determine, GMM is exclusive to SAS/ETS.
SteveDenham