Not sure why you contend that Romans 8:26-27 in the NIV is not proof text to what you believe.I'm KJVP, and don't bother with other version of the Bible generally. Speaking in tongues in private worship is every bit is clear in the KJV (1 Cor 14) as it is in the NIV, so no issue there at all. Speaking unto God and not unto Man is Prayer no matter how you slice it. Paul says he speaks in tongues more than y'all, BUT IN THE MEETINGS he communicates in the common tongue.
I can only suggest to you to reconsider your reading of 1 Corinthians 14:2, because 1 Corinthians 14:28 is key. If verse 28 is supposedly read and applied as speaking in tongues but if no interpretation, to be commanded to be silent, and yet Paul says not to forbid speaking in tongues in verse 39, why can Paul command that person to be silent when there is no interpretation in verse 28? See the conundrum?
If one believes one can speak in tongues or pray in tongues quietly while others on either side of them are trying to listen to what is going on in the assembly, they are sadly mistaken. If churches do not allow people to talk in church, as it would be distracting and hard to hear, even though we have an electronic sound system, why would anyone be allowed to pray in tongues quietly in the days of Paul in church?
So obviously, verse 28 means no speaking in tongues at all when there is no interpretation. BUT, that does not align because if the Spirit is bothering to manifest speaking in tongues, then why would Paul command Him to be silent, even when supposedly praying? That is nonsense as it is also going against not forbidding anyone speaking in tongues.
So verse 28 is about a foreigner speaking out of turn for why there is no interpretation of that tongue because the holy Spirit is not manifesting that tongue. When you have 2 or 3 speak in tongues while one interprets in verse 27, newcomers & visitors may not understand what is going on and stand up to speak out of turn. That verse 28 is Paul's way of saying that this is a foreigner speaking out of turn and not speaking in tongues for why he is commanded to be silent because and Paul says this; he speaks to himself and to God, meaning he understands what he is saying as God does; not that he is speaking to himself and speaking to God as well.
That is how you are to read verse 2 because him speaking to God is not saying he is speaking TO God but that God understands what he is saying, but the man speaking does not understand what he is saying as in the spirt, he is speaking mysteries. There are no mysteries to God but only the man speaking in God's gift of tongues is a mystery to himself. That is why Paul says for those who speak in tongue to pray that God will raise up someone to interpret that tongue for the tongue speaker so that he may understand what is being manifested by tongues so that tongue will be fruitful to himself as well and not just to others.
This is why Paul from the beginning of that chapter is exhorting prophesy over all gifts and began comparing tongues against prophesy because tongues is not a stand alone gift because it has to come with interpretation for the tongue speaker and others in the assembly..
1 Corinthians 12th chapter lays the ground work about the gifts manifested in the assembly, and they are not gained by seeking another baptism with the Holy Ghost as verse 13 testify for we are all to speak the same thing of having that one drink of the One Spirit by which we were baptized by at our salvation moment when born again of the Spirit. Verses 19-21 is proof for why tongues are not for private use also.
19 And if they were all one member, where were the body? 20 But now are they many members, yet but one body. 21 And the eye cannot say unto the hand, I have no need of thee: nor again the head to the feet, I have no need of you.
Modern day tongue speakers list all the benefits for tongues for private use without realizing that they are saying they have no need of the body of Christ. That is why God's gift of tongues are not for private use as it is to profit the body withal.
1 Corinthians 12:4 Now there are diversities of gifts, but the same Spirit. 5 And there are differences of administrations, but the same Lord. 6 And there are diversities of operations, but it is the same God which worketh all in all. 7 But the manifestation of the Spirit is given to every man to profit withal.
So the Holy Spirit does not need to pray in tongues or utter anything in that regard. Romans 8:26-27 is for all believers for why there is no need for the Spirit to pray out loud in tongues, and John 16:13 in ALL Bibles says He cannot speak from Himself in that way either.
Now you say Romans 8:26-27 does not support tongues and John 16:13 limits how the Holy Spirit will speak by only speaking what He hears, then there can be no praying out loud from the holy Ghost for tongues in private use.
So what is happening? Apostasy because these kinds of supernatural pagan tongues have been in the world before Pentecost as gibberish nonsense that even the Bible confirms in Isaiah 8:19. This is why John says to not believe every spirit but test them as He dwells in us but that which is out in the world and coming over us later in life as a saved believer, that is not the Holy Spirit ( 1 John 4:1-4 ) and we are to even test the tongues they bring ( 1 John 4:5-6 ) If a believer believes they can receive the holy Spirit again, God will permit that strong delusion to occur for why they are getting tongues without interpretation and thus assumed for private use ( 2 Thessalonians 2:9-15 with verses 13-15 as reproof for the lie in verses 9-12 ).
Matthew 6:7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking. 8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.
With Romans 8:26-27, this is because of Jesus Christ searching our hearts & knowing the mind of the Spirit is how the Father knows everything before we even ask in prayer. This is written to assure us hen we are overwhelmed and we do not know what or hoe to pray, we can rest in His words that the Father knows.
Ask Jesus Christ for wisdom & discernment in normal prayer because how you apply 1 Corinthians 14:2 to mean, is running against the truths in other scripture.