Dear Luc
As you said,mexican garcinia is limoncillo.It is not Garcinia intermedia nor Rheedia edulis(Some people say both are same and same say they are different).One article(
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3040103/) says that Rheedia edulis (synonym: Garcinia intermedia) is known as “waiki-plum” in Belize, “arrayán” or “palo de frutilla” in Guatemala, “chaparrón” in El Salvador, “Caimito” in Honduras, “jorco” in Costa Rica, “sastra” in Panama, and “limoncillo” in Mexico. This species is also cultivated in Brazil and The Philippines where it is known as “limăo do matto” or “berba”, respectively.
There are other two limoncillo's-Cassipourea guianensis and Melicoccus bijugatus.
I request the forum to find out a proper scientific name for Mexican Garcinia (or Rheedia,if it belongs to this)
I wish to grow this.I will give you some seeds from India.