As others have said, the problem with Limoncillo is that the term is more in use for guinep/Spanish Lime and also has no semantic association with garcinia/mangosteen but rather with lemon and lime. Too many unique fruit names for consumers to keep track of, it is not in its own genus! As for 'Lucosteen' that sounds like medication or a sports drink.
Anything with 'mangosteen' in it will probably end up with too many syllables, and from a taxonomy point of view, really only the purple mangosteen should be associated with that name (garcinia mangostana).
I'm all for Luc getting credit in the scientific sense (G. vleerackeii) but extending that to the common name is a bit unrealistic from the perspective of marketing and relate-ability to an international market. Had he bred it as a cultivar then it is a different story.
Luc, have you asked any indigenous people what they call it? Limoncillo sounds 100% Spanish in etymology. I believe they speak Nahuatl in Puerto Vallarta? I thought to propose the neologism 'cozticotl' = yellow fruit, but it is a bit of a mouthful.
My suggestions would be to adapt the name 'garcinia' with a Mexican(Spanish) or Nahuatl suffix:
Garcinillo
Garcinilla
Garcinoro (the 'oro' here means gold)
Garcinotl
Yes, I know letter 'L' is silent in Spanish, but in English it is pronounced, right? Maybe Garcinillo is the best of these options.