Agree, 1 Cor is about languages, so if it does not meet the criteria for a language it is not a language.
Paul makes it clear that those speaking in an unknown tongue are doing so through the operation of the spirit. Their spirit is conversing with God:
For he that speaketh in an unknown tongue speaketh not unto men, but unto God: for no man understandeth him; howbeit in the spirit he speaketh mysteries. 1 Cor 14:2
Paul also says that when he prays in an unknown tongue his understanding is unfruitful. If he is speaking a language he knows why would he not understand what he is saying?:
For if I pray in an unknown tongue, my spirit prayeth, but
my understanding is unfruitful. 1 Cor 14:14
I thank my God, I speak with tongues more than ye all:
Yet in the church I had rather speak five words with
my understanding, 1 Cor 14:18-19
If what you are expressing is that Paul is referring to people speaking known languages, just not languages known to the individual, that could be possible. But would not change the fact that it is being done supernaturally through the operation of the Spirit.
If this is the case, it would be impossible to ascertain if one's speaking in tongues were authentic or not. It would be virtually impossible when one considers that according to sources on the Internet "there are roughly 6,500 spoken languages in the world today. However, about 2,000 of those languages have fewer than 1,000 speakers."
If unknown tongues are current and past languages spoken throughout the world God certainly has a variety to choose from to impart edification to His church.