The issue with the Calvinist/Arminian/Neither soteriological debate isn’t about embracing Scripture, because this soteriological debate is among those who already embrace Scripture, but have different interpretations of what Scripture says.
This is similar to the credobaptist/paedobaptist debate, where both sides already embrace Scripture but have a different understanding of what the Bible teaches.
Both Calvinists and Arminians believe in predestination, but they differ on whether predestination is based on foreknowledge. Both Calvinists and Arminians believe that Jesus died for sinners, but they differ on whether Jesus tasted death only for the elect or for everyone without exception. Both Calvinists and Arminians believe that God shows grace to sinners, but they differ on whether this grace is irresistible or resistible.
And needless to say, Calvinists and Arminians may very well have different definitions for words such as “sovereignty”, and “foreknew”, just like Baptists and Presbyterians have different definitions for the word “baptize”.
(If Arminianism is true, it means that some Christians chose to believe in Calvinism instead of Arminianism out of their own libertarian free will, even though they could have chosen otherwise. If Calvinism is true, it means that God predestines some Christians (whom He has elected before the foundation of the world and whom Jesus died for) to be Arminians, and these Arminians whom God has elected before the foundation of the world could not have chosen otherwise.)
I find your summary to be very accurate.