Sadly, people are reluctant to give away their LS because the legit ones are always too full to join even for the people that know them! Try and ask your friends for THE infamous hunt LS's name that is most popular on gilgamesh and then search it on Lodestone to find the Leaders/Master and send em a whisper for invite every time you need to get in.

Thats the best tip you'll have, worth more than actually getting a 1-time invite