The same happened to me too. Tarquin was missing for large parts of act 2 and never appeared at Stonegarden. At some point he returned to the Lady Vengeance and never offered the quest to me.
I am way past this point now without the ability to do anything with the two quest items, but I really hope it will be fixed for my second playthrough, so I can at least do the quest then.
A fix so quests like this can not be missed as easily and won't become unavailable entirely because an NPC is not where he is supposed to be (or in a different location later on) would therefore be very much appreciated!
There should really be no reason why I can't just give both pieces of the sword to Tarquin later on if I have them in my inventory already, even if the first step of the quest bugged.