I have the ability to convert 'some' dropped set piece equipment to both of those styles.
What puzzles me is that there are other set pieces that I can't convert.
It matters not whether the piece starts off as bound to me or not.
For instance - I have 2 Endurance Set daggers that started off as Ebonhart Pact that I can convert to Imperial and Morag, and both of those daggers were bound to me before I tried to convert them.
I have a Night Mother staff that was looted, and isn't bound to me, that I can't convert even after I launder it.
I have a Necropotance staff that was a drop item that is bound to me, that I can't convert either.
But I can convert set piece jewelry to Imperial or Morag with no trouble.
So: What are the hard and fast official rules that determine whether I can convert or not?
I mean, it's not like the rules can be arbitrary, considering that I bought the Imperial Package and converting equipment was part of the deal of the sale.
After all.... ZOS wouldn't do something slippery to us, would they?

The problem with society these days is that no one drinks from the skulls of their enemies anymore.