Here's the best way I know how to answer the objections with respect to preaching, the great commission, etc. If it works for you, great, if not, that's okay, too.
First, let's assume the position of election is true. Let's assume that man cannot possibly of his own free will change his self-centered and sinful inclination and therefore would never want to repent and put his faith in Jesus. The fact that man cannot, of his own free will, change his inclination is effectively saying the same as he cannot choose to put his faith in Jesus. It is impossible, because man will not choose something he is inclined NOT to choose. God must first change his heart, after which it is impossible for him not to want to choose to put his faith in Jesus.
To repeat, let's assume ALL of the above is true.
Now -- is the following not ALSO true?
1. People are sinners and should repent.
2. If you don't repent you will not be saved.
3. If you confess with your mouth Jesus is Lord and believe in your heart that God raised Him from the dead, you will be saved.
4. Whosoever believes in Him will not perish but have everlasting life.
5. If you don't believe, you are going to perish.
So when people preach these things, why are they any less true if God has elected to make the message effective unto salvation for only SOME of those who hear it? Aren't all the above statements true for all, regardless? Yet why should one marvel at the fact that only those who God has appointed to eternal life are moved by the message?
Acts 13:48 "When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed."
------------
On a more personal note...
I notice that Acts 13:49 does NOT say "But since some did not believe, the apostles stayed there several years and preached and preached, warning them over and over again of the dangers of hell in order to win their stubborn souls for Christ."
I have nothing against dogged persistence in preaching, in the hopes that those who vehemently reject Christ will repent. I believe that if the Spirit moves someone to do that, there must be a good reason for it.
But I would point out two things:
1. The language of Acts 13:48 sounds very matter-of-fact, at least to me. The most comfortable follow-up would almost be, "And those who were not appointed for eternal life didn't believe. And that's the name of that tune."
2. Is it not ironic that this "dogged persistence" is an effort to change the hearts (the inclination) of those to whom one preaches? We're not giving them a choice to make of their own free will. We're desperately trying to persuade them -- to change their inclinations so that they will change the desires of their heart and WANT to make the RIGHT choice.
So if we (the editorial we) believe we should spend the time and effort to change the hearts of listeners, why do we object to the idea that God must first change our hearts (our inclination) before it is possible for us to believe in Jesus?
That leads to the next question. If we believe we have been successful in persuading someone -- successfull in changing his/her heart or inclination -- to whom do we REALLY assign the credit for that change? I'm not asking who you verbalize as deserving the credit, but to whom you REALLY assign most of the credit. After all, if "salvation by free will choice" is true, and God does not have to change the inclination of the heart, then YOU (the editorial you) did most of the hard work in convincing that person to change his/her heart.
That's why I believe "salvation by free will choice" is all about man's pride, not about God, and I believe it is pride both from the perspective of the person who believes he is saved by choice, and the person who preaches to those he wants to be saved by choice.