According to your tree Italic is a Celtic language? So maybe people viewed it as adopting a new dialect, merely a matter of convenience when dealing with traders.All Insular Celts (R1b-L21) spoke Q-Celtic languages originally, and P-Celtic probably started replacing Q-Celtic in Britain when the Hallstatt migrants arrived c. 500 BCE, followed by Belgic tribes in the first century BCE. As you explained it yourself, Q-Celtic speakers could easily have adopted the new Gaulish dialect and turned it into Brythonic if the continental Celts enjoyed a higher cultural prestige. The same thing happened when Latin replaced (quite easily) Celtic languages in northern Italy, Gaul, Iberia and Britain owing to its higher prestige. This can happen quickly when languages are relatively close to one another (same family). That is also how Arabic came to replace other Semitic languages in the southern Middle East and North Africa (e.g. Coptic Egyptian and Berber).
Rather than viewing continental Celtic as a single language, it should probably be viewed as a language family, as without a nation state it would have fragmented into a thousand different dialects.