What about this verse in particular?
This highlighted verse seems to imply that (at least) some of those who spoke in tongues spoke in a language that only God could interpret. Couldn't the pentecostals use this verse to make a valid case for their "gibberish"?
The mysteries of God are "another language"... Look at the parables of Christ, the prophecies, etc.. They are not to be taken literally.. This are the "tongues of the angels" : The doctrine of God.
If you examine 1 Cor 13:1-3 you will see that Paul is using exaggerated language to bring home his point that love is greater than the gifts. For example in 1 Cor. 13:3 he speaks about having all knowledge while at the same time he knew that he could not have all knowledge as knowledge was 'in part' (1 Cor. 13:9). What he is saying in these verses is, in effect, "Even if I could jump over the moon and had not love then I have nothing". So, he is not saying he could speak in tongues of angels but that 'even if' he could and didn't have love then he had nothing. There is no such thing as tongues of angels.
Also, the reason tongues sounded like mysteries at times was simply because foreign languages do sound like mysteries to us ... that is why Paul said that without an interpreter the speaker was to keep it between himself and God as no one is edified unless there is understanding.
Paul makes reference in verse one to the "tongues of angels" ..This is the thing to which he refered as "the tongues of angels" , the knowledge of God, the knowledge of the spiritual world , and the knowledge of this world "the tongues of men".. I was not refering to the tongues of angels as a non-human language..