Tips for anyone who got a 3-slot weapon:
Use the given materials to upgrade it to stage 3, each upgrade has a chance to open a gem slot.
Join Radiant Ring Crafting Guild
Send any Ore from other characters to your character with the weapon
Place an order for Special Ore
If you have any Ore on hand, Order the maximum amount of Guild Supply boxes
Max out your Radiant Ring Guild level
At max guild level you can order account bound legendary gem hammers
My character had 4 slots after upgrading to stage 3 so I don't know the legendary gem hammer requirements for slot 4 but:
Slot 5 = 15 legendary gem hammers
Slot 6 = 21 legendary gem hammers
Slot 7 = 22 legendary gem hammers
Slot 8 = 22 legendary gem hammers
Crafting legendary gem hammers in Radiant Ring:
9 Hammers - cost: 94 Special Ore, 31 Rare Element, 48 Soulstone Crystal, 12 Moonstone Crystal, 48 Sacred Crystal, 12 Elysian Crystal, 3 Gold
21 Hammers - cost: 220 Special Ore, 72 Rare Element, 112 Soulstone Crystal, 28 Moonstone Crystal, 112 Sacred Crystal, 28 Elysian Crystal, 7 Gold
This is the most cost effective way to get legendary gem hammers if you're unlucky on slots.
I do have a slight warning for impatient folks: If you have no Ore to start with it will take awhile to get the necessary amount of Ore to not only craft the Guild Supply boxes to max out your Guild Level but also to craft the hammers themselves.