Huh ? You lost me friend.
Your quote below.
I believe the Father and Son sends the Spirit into the redeemed to effect the drawing, so all Three Persons of the Godhead are involved in drawing. In fact the drawing entails I believe being born again by the Spirit.
The redeemed already have the Holy Spirit in them so there is no need to send the Holy Spirit again just to effect the drawing from inside the believer... if I am understanding your post correctly.
How do we prove or reprove the notion that "all Three Persons of the Godhead are involved in drawing".? I can find no scripture testifying to that effect but there are scripture singling out the Father plainly as the One doing the drawing as that drawing is done according to His will.
John 6:44
No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day. KJV
Who gives to the Son to save sinners? Whose will is it for the Son to save sinners given to Him?
John 6:38 For I came down from heaven, not to do mine own will, but
the will of him that sent me. 39 And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. 40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day. ~ KJV
So how does the Father give to the Son to save them? Scripture says the Father hides the truth from the wise & prudent & reveals the Son even to babes.
Matthew 11:25 At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. 26 Even so, Father: for so it seemed good in thy sight. 27 All things are delivered unto me of my Father: and no man knoweth the Son, but the Father; neither knoweth any man the Father, save the Son, and he to whomsoever the Son will reveal him. ~ KJV
There is a role that signify belonging to the Holy Ghost as He is called the Comforter. John 14:26
Just as Jesus Christ is the only One that dies on the cross for our sins; not the Holy Ghost nor the Father.
So there is a role that the Father performs & scripture gives the Father that sole credit of doing the drawing. When scripture plainly has Jesus testifying that no man can come to Him except the Father draws him, then I believe He meant what He has said as no one else is doing the drawing, but the Father.