That is convincing.
According to Mallory the closest linguistic neighbours to Armenian are Phrygian, Thracian and Greek. The origin of the Armenian branch is therefore indeed to be found in the (southeastern) Balkans. I think they may have travelled from west to east over Anatolia slightly before Phrygian around 1200BC swept Hittite away (which was in Southern and eastern Anatolia replaced by Luwian-speakers, also Anatolian) or in the same wave as Phrygian, because Armenian contained borrowings from Anatolian (which Mallory says).
So on linguistic grounds, there is a lot to say that Armenian came from the Balkans in the west to travel over Anatolia to the east not later than 1200BC.