Firstly, we are talking about the assembled Church here. So in my opinion, outsiders would not come into play here. Secondly, What I believe is being addressed is offering prayer in the vernacular. Here is an example. In the back of my 1599 Geneva is a list of archaic words. If someone prayed using these words, the majority of us, including myself, would have no understanding. Leaning toward being charitable I would not use them to avoid leaving many of my brethren without understanding. I would also add that it would be lacking humility and charity if one wished to exercise their vast vocabulary before others without consideration for them. God will understand them, but how can others add the amen to what they don't understand? I would especially be careful with English as a second language situations.
First of all, I don't pray in "King James English." It is unnatural for me to do so because I don't talk that way and I think it would be fake for me personally to do so. However, my point in my previous post is that "King James English" is still English. It is not an unknown language. So I don't think that your quote from the confession applies. There are words that may not be understood but that doesn't make it an unknown language. I can use words in my prayers from a modern version that are not understood but I am still speaking English.