That's what traducianism teaches. God made the method of pro-creation for all lviing beings, so that they pass on their life to their offspring.
The creationist theory of the souls maintains that God actually creates a soul at the moment of conception.
I have looked at your Puritan link (you call them "real" Protestants?) and it is essentially no different than the Protestant link I provided. Your ;ink is decidedly creationist in line with the Catholic and Reformed way of thinking (mine was neutral).
But there is no insuation that God created souls before the world, and stored them for future use (like some pagan-influenced rabbinical 'musings' claim).
That isn't the same thing as saying God created all souls in the beginning
Gnostics, pagans and Pharisaic Jews believe that. Christians don't.
Earlier I stated that our Lord's soul must have existed in Melchizedek
I don't know why you would do that. Hebrew 7:3 states "Without father, without mother, without genealogy...that should be a hint that it is not Christ, for Christ has a Father and a Mother and royal genealogy (related to King David); the Gospels even start with His genealogy!
insuation=insinuation