Splintering is not a reforge quality, that quality is exclusive to the Wrong/Shame Loot system.
UO Stratics *New* | Runic Re-Forging
As noted in the link, even if you add Slaughter you don't have a chance at splinter.
The "All Types" are what you have a chance of getting on the any item you reforge using said title.
Then Weapons are qualities that only weapons have a chance at getting, Armor to armor, shield to shield. Sorry to be the barer of bad news for those wanting to reforge splintering weapons :/