It's hasn't just been adopted by Arminians. It is the predominate view of many different theologies. Unitarians use it too. Most people don't actually understand it. It is the concept of the Eternal nature.
There are many reasons why it is used today. Election is one of them. I don't see a contrast in how it is used between 1 and 2 in your list. Same goal. To explain the Eternal nature of God's knowledge while insisting God is unchanging.
In view one foreknowledge, men are elected based on God's foreknowledge of them.
Election and Foreknowledge
An Essay By
Fred Zaspel
Definition
Foreknowledge, with reference to God, connotes foreordination. The doctrine of election affirms that God chose those whom he would save.
Summary
The question at issue here concerns the meaning of foreknowledge with respect to election, particularly in
Romans 8:29 – specifically, whether “whom he foreknew he predestined” indicates that God chose whom he would save based on their foreseen faith. Following a brief introduction to the question this essay will sketch out the deciding considerations: the biblical characterization of election, the ground of God’s knowledge, the meaning of “foreknow” with reference to God in Scripture,
Romans 8:29 in context, and finally some considerations in
Romans 8:29 itself.
Introduction
The doctrine of election affirms that for purposes known only to himself God chose those whom he would save. He did not choose them because of anything about them but for his own “good pleasure” (
Matt. 11:25-27). The Arminian doctrine of election often argues to the contrary, that God chose whom he would save based on foreseen faith – that looking ahead, God saw who would believe and on that basis chose to save them. That is, according to the Arminian doctrine, God “chose” us but only because we first chose him.
What you state makes me think that is what you hold
In the second view Corporate election
II. Election Corporate A second aspect of election is implicit in Paul's Ephesian doxology: the election to salvation is corporate as well as Christocentric. The corporate nature of election has been noted by many. In his comment on Ephesians 1:4, previously cited, Lightfoot writes, "The election of Christ involves implicitly the election of the Church."3 2 Westcott comments on Ephesians 1:4, "exelexato ] He chose us (i.e. Christians as a body v. 3) for Himself out of the world."3 3 Bloomfield comments on Ephesians sians 1:5, " ... the Apostle has here no reference to the personal election of individuals.... 1134 Lange comments on Ephesians 1:3 ... "us" should be taken in its wider meaning ... and should not be limited to the Apostle ... nor to the Jewish Christians, but applies to his people, all men, who have become or will become Christians.35 The corporate inference of Lange's words above is substantiated by his comment on Romans 8:28-30, " ... Christ is the elect in God's real kingdom in the absolute sense, so that all His followers are chosen with Him as organic members, according to their organic relations (Eph. i)."3 6 Obviously, the corporate body of the elect is comprised of individuals. But the election is primarily corporate and only secondarily particular.