What about the theory about the Picts originally speaking a not-IE language?
From the inscriptions found in Scotland it seems that they were at least bilingual, I've read, that have been found inscriptions in Celtic language and in an unintelligible non-IE language. If it's true then they spoke Celtic as acquired language to communicate with their neighbours of the south, while they continued to speak the ancestral language, until it was totally replaced by Gaelic centuries later.
From the inscriptions found in Scotland it seems that they were at least bilingual, I've read, that have been found inscriptions in Celtic language and in an unintelligible non-IE language. If it's true then they spoke Celtic as acquired language to communicate with their neighbours of the south, while they continued to speak the ancestral language, until it was totally replaced by Gaelic centuries later.