Go to achievements and look up the top endgame shells on your server. Either send a tell to someone with a sack or check their LS websites.
You can also just keep seeking in Dragon's Aery, Valley of Sorrows, and Behemoth's Dominion until you spot a bunch of people in zone, then just go there and ask whomever gets claim.
Getting timers is easiest after a server reset because the windows are open as soon as the server goes up.
Alternatively, MNK/NIN can duo Adamantoise and probably Behemoth on a level 80 cap. Free beats paying for the drops any day of the week.
You can also do KS99 for the drops. Wyrm can be done with a PT of 6, and the Behemoth with not much more than that. Need a bunch of BLMs for easy Tartaruga Gigante, tho.
Overall, the easiest and cheapest path is to get claim on Adamantoise and Behemoth until they drop, then get some friends to do a Wyrm KS99 run.
Good Luck to you, sir.