I stumbled across this about an hour ago, and first off I'd like to say this isn't without sacrifice, but it does beat spending 2,000,000g or farming 30+ Adamantoise and wanting to kick a kitten every time it doesn't drop.
The sacrifice in hand is the Genji Glove (Missions 51, 62, 63) of which there are only three in the game. If one of these is upgraded to Star Level then dismantled you get one Tear of Woe and one Trapezohedron.
You lose the ability to pass the 99,999 cap with a character, but gain the ability to upgrade to someone's Ultimate Weapon without the frustration of a 1% drop rate.
If this had already been posted I apologize, but didn't see any notice of it anywhere.
XI Wiki


