This is not the first time I've seen people get in trouble by trying to make 'the elect' a distinct and separate group from all believers.
I haven't heard it in a while, but it used to be popularly taught that 'the elect' was Israel. Easily debunked by scripture when you see gentiles also addressed as 'the elect' (it's been a while, I have to remember the scriptures). I think they did that in order to defend a certain brand of end-times thinking.
Right off, I'm not familiar with the Thess. reference you're making.
Here we see the scripture specifically given to the 'elect'. It seems to me that if the elect is not the whole body of Christ, then the rest of the Body, was not given these instruction, including the last one quoted and those beyond.
Col 3:11 Where there is neither Greek nor Jew, circumcision nor uncircumcision, Barbarian, Scythian, bond
nor free: but Christ
is all, and in all.
Col 3:12 Put on therefore, as the elect of God, holy and beloved, bowels of mercies, kindness, humbleness of mind, meekness, longsuffering;
Col 3:13 Forbearing one another, and forgiving one another, if any man have a quarrel against any: even as Christ forgave you, so also
do ye.
Col 3:14 And above all these things
put on charity, which is the bond of perfectness.
Col 3:15 And let the peace of God rule in your hearts, to the which also ye are called in one body; and be ye thankful.
Col 3:16 Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.
Col 3:17 And whatsoever ye do in word or deed,
do all in the name of the Lord Jesus, giving thanks to God and the Father by him.
Col 3:18 Wives, submit yourselves unto your own husbands, as it is fit in the Lord.