As I understand it, Arminius believed that humans have natural free will even in a state of sin apart from grace, while Wesley believed that it takes prevenient grace to restore free will. However, Wesley can be interpreted in a more strictly Arminian manner, and as you note that is the path many modern Methodists have taken. But in the 1830s and 40s at least Methodists were still commonly distinguishing their position from that of someone like Finney.
Wesley and Fletcher chose to call themselves “Arminians,” and those of us on the more Augustinian side of the Wesleyan tradition regret this. I sometimes say that I’m an “Arminian by default.” In other words, I reject certain Calvinist claims, but I do not see “Arminian” as the best way to describe my theology.
John Wesley was not the most profound or nuanced theologian in the history of the Church. He had a good dose of 18th-century breeziness and practicality, which often led him to skate over some very difficult issues without defining them clearly. And there’s no denying the fact that he didn’t like Augustine and thought that Augustine had probably slandered Pelagius badly. His theology became more “Arminian” later in life–earlier on he made more common cause with Calvinist evangelicals.
I don’t regard Wesley as infallible, but I do think that the basic concept of universal prevenient grace is the best way I’ve found so far to preserve the key Augustinian claims about human sinfulness and the sovereignty of grace while not blaspheming against God by putting limits on His mercy.
I don’t have an opinion on that subject. God is sovereign, and God is merciful. I don’t need to call Him to account for how He chooses to offer grace, but I am confident that He desires the salvation of all. I do not believe in “irresistible grace” in any sense. So I’m an Arminian in the sense that the difference between a person who is saved and one who is lost is going to come down to the fact that one of them closed himself off from God’s grace in a persistent and resolute manner and the other opened himself to it.
Edwin
P.S. I responded to your OP in my post #43.