If it's not a collective action then it is not being reflexive/reciprocated. One person (or group) cannot sing while the rest sit and listen and have the singing be reflexive and reciprocated. So heautas as used in the context of Eph 5:19 is collective singing.
A reflexive pronoun is used with another noun/pronoun when something does something to itself.
John hit himself - reflexive for John did something to John
"They hit themselves." doesn't have to mean everyone hit himself at exactly the same time. English has it's version of a reflexive, and what you say isn't true of English, or of the English translation of Ephesians 5. The quotes I just got demonstrate that your assertions about this Greek word isn't true. When people have a conversation, they don't usually speak in unison like they are singing a song. That would be a miracle or something supernatural if such a thing spontaneously occurred. Suggesting that Christ's opponents did so based on the use of this Greek word, when questioned about John's baptism, is a ridiculous interpretation of scripture.
You are also breaking your own rules of hermeneutics with Ephesians 5:19. If silence forbids, then you can't allow for singing, because the passage says 'speaking' to yourselves in psalms, hymns, and spiritual songs. Haven't you argued that the melody is in the heart? Like you pointed out about I Corinthians 14:26, having a psalm could mean reading a written psalm without singing.
It's really inconsistent to think 'hath a psalm' means reading a psalm, while Ephesians 6 is speaking about singing. Ephesians 5 explicitly says 'speaking.' I Corinthians 14 doesn't say whether speaking or singing is in view. So there is a stronger case for solos being sung if you want to take your rigid view.
The real problem with your approach is this 'silence forbids' idea. What you are doing is speaking where scripture is silent. There is a lot of other scripture, though, that you aren't considering, Revelation, and the Old Testament. Both of these refer to instruments.
The real issue seems to be that you go to a church that you believe has it figured out. You argue in the direction of whatever your church tradition does.
So how can one be singing to himself if he is not singing at all during the time frame the song is taking place?
There is no reason to think it has to take place during the duration of one song, since it says 'in pslam
s, hymn
s, and spiritual song
s". It's not talking about just one song. If I speak one psalm, and another brother speaks a hymn, etc. that situation fits the description. Paul doesn't command that every individual has to do so in one meeting.
Speaking congregationally would fulfill the same requirement. I don't take the rigid silence approach, so I allow for singing in both cases.
I Corinthians 14 clearly allows for either a solo or individually speaking out a psalm. I don't take this rigid version of the regulative approach, so I believe singing is allowed, as long as it is done unto edifying.
Your assuming that if an individual 'hath a psalm' that he suggests it to be sung congregationally has no support in the text. I'm not against that, but Paul says 'every one of you hath a psalm'. If you take the silly rigid silence approach that you use elsewhere, you shouldn't be reading suggesting congregational singing into the text. Other things mentioned in the text aren't done in unision (teaching, tongues, sharing revelations, or interpretations.) These other activities are to be done in a turn-taking manner rather than in unison.