All the explanations you gave are not a part of the songs. You're rationalizing them.
No song comes with full theological explanations.
The point is that what they DO say is not AT ALL incompatible with Calvinism. It may be that the reason you think what they say is, is that you don't fully understand Calvinism.
There is not a Calvinist in the world who thinks that Christians cannot accurately sing, "Whosoever surely meaneth me."
There is not a Calvinist in the world who thinks that he did not "...decide to follow Jesus."
We sing those songs with as much fervor as you do.
They are accurate. They are TOTALLY consistent with Calvinism.
We understand something that the Arminian DOESN'T understand when he sings that song- that the REASON we have decided is because God has made us willing.
Does this sound like Calvinistic theology?:
I will hasten to Him, hasten so glad and free;
Jesus, greatest, highest, I will come to Thee.
I will hasten, hasten to Him, hasten so glad and free;
Jesus, Jesus, greatest, highest, I will come to Thee.
COMPLETELY.
ITL, Calvinists believe ALL OF THAT.
We simply understand that the fervency with which we hasten to him comes FROM HIM. He has conquered our hearts with his love and we cannot BUT hasten to him gladly and free.