Riley, Finney was not a private Calvinist. I do not believe he was even a Christian, or if he was, he was at best severely deceived. You can google him for more.....this is a quick link on my part, I don't have time to look more now, but some of his quotes are unbelievable, this doesn't even scratch the surface.
Whatever the subtle differences between true gospel and hypercalvinism, and whatever your understanding of moral responsibility and election, and how to evangelize, and whatever terminology Finney used, his understanding of volition and inability was not Edward's understanding, even if terminolgies appear to be similar. Finney did not even believe in original sin or total depravity or imputed righteousness. There just is no cause and effect blame to Edwards for the later practices of Finney.
Finney Systematic Theology quotes
Quotes from his heretical Systematic Theology.
ORIGINAL SIN
"We deny that the human constitution is morally depraved, because it is impossible that sin should be a quality of the substance of the soul or body. It is, and must be, a quality of choice or intention, and not of substance. To represent the constitution as sinful, is to represent God, Who is the author of the constitution, as the author of sin. What ground is there for the assertion that Adam's nature became in itself sinful by the fall? This is groundless, not to say ridiculous, assumption, and an absurdity."
JUSTIFICATION BASED UPON SANCTIFICATION
"We see that, if a righteous man forsake his righteousness, and die in his sin, he must sink to hell. Whenever a Christian sins he comes under condemnation, and must repent and do his first works, or be lost."
REGENERATION
"Regeneration implies an entire present change of moral character, that is, a change from entire sinfulness to entire holiness."
OBEDIENCE
"That which the precept demands must be possible to the subject. That which demands a natural impossibility is not, and cannot be, moral law. To talk of inability to obey moral law is to talk nonsense."
ENTIRE SANCTIFICATION
"It is self-evident, that entire obedience to God's law is possible on the ground of natural ability. To deny this, is to deny that a man is able to do as well as he can. The very language of the law is such as to level its claims to the capacity of the subject, however great or small that capacity may be. 'Thou shalt love the Lord thy God with all thy heart, with all they soul, with all they mind, and with all they strength,' Here then it is plain, that all the law demands, is the exercise of whatever strength we have, in the service of God. Now, as entire sanctification consists in perfect obedience to the law of God, and as the law requires nothing more than the right use of whatever strength we have, it is, of course, forever settled, that a state of entire sanctification is attainable in this life, on the ground of natural ability."