Evangelicals have gommed up the words 'saved' and 'lost' by always willy nilly with a broad brush applying the eternal sense to them. Do you honestly think that Paul was praying for all Jews to go to heaven? Did he also pray for all non-Jews to go to heaven? Saved means delivered, rescued. Consider the words of the Holy Spirit through the apostle Peter:
40 And with many other words he testified, and exhorted them, saying, Save yourselves from this crooked generation. Acts 2
Deliver, rescue yourselves from this crooked generation for the wrath to the uttermost is soon to descend upon it for all the righteous blood shed on the land.
6 Give not that which is holy unto the dogs, neither cast your pearls before the swine, lest haply they trample them under their feet, and turn and rend you.
Mt 7
That's not a strawman. Anyone who says we are not pre-chosen and that it is dependant completely on man's own free choice believes man has something to do with his salvation.
I don't know anyone that believes salvation is "completely on man's free will choice". By you insinuating that someone believes that and then saying they are wrong is the very definition of a strawman.
God will save His elect, but they won't be saved without prayer.
Go figure.
We pray because God is sovereign.
If He were not, there wouldn't be much point in praying to Him.
"Do your best, Lord!
I know you can't override his stubborn heart, but could you maybe try?"