It would be indeed heartless and evil to NOT preach the gospel to anyone who would listen, because God has men everywhere, of every station, of every age, of every race, of every nation, and if we say he doesn't we are liars and do not know the Saviour of the world. John 4. Many missionaries were predestinarian e.g. William Carey and many others. There were also calvinist preachers, who preached predestination and people got saved at the same sermon. People get saved with non-calvinist preaching, no denying of that.
But there is a proper missionary activity and an improper one. The improper one consists in trying, by all means (not that we shouldn't use means) to make people go to church and raise their hand, walk up to the altar or say a prayer after a 2-3 minute conversation. This is called "easy believism", free-will doctrine taken to an extreme, and is very dangerous, because it gives those "converts" a false sense of security from their own decision or little prayer, but those people, while interested for a while and assent to the doctrines of the gospel, fall off and have never repented. Some missionaries nevertheless do this car salesman approach to get support, because their funding is based on their success , many also do it for their own glory Phil 1, and some really do it honestly, but it is futile, because it puts too much stress on a short experience and ignores repentance and discipleship. The Bible teaches us to plant, water and wait for fruit James 5. There needs to be a lot of teaching, preaching and praying to get people into the faith, whether or not you believe in free will or universal atonement. Some may get saved from a single sermon, but that is very rare.
RE: Jesus died for the elect. This doctrine is misunderstood or viewed from the wrong angle. Jesus died for MANY, for millions upon millions.That is comforting. It is not as if he died for no one. But if we say that he died for every single person, we don't improve the situation either here on earth or at the judgment, when most will go to hell, one bit, because when a person is saved its because he believes Jesus died for him, a sinner, not for every single person, thus at the time of conversion he is "limiting" the atonement to himself, he isn't thinking about chances, whether or not he is among the elect, but he KNOWS Jesus died for him. Furthermore, many believe that because Christ died for ALL, God will somehow save them in the end and they dont need to repent and thus perish. If it is up to me, I can delay till my deathbed and then accept Christ and repent etc.
Then we arrive at the next pitfall - If God loves all and is Omnipotent, why doesnt he save them all? He tells us to love in deed and truth, but if we say he loves all and he doesnt do all to save them, how is that real love? We are left with an even more troubling question. The reality is that most will go to Hell. It is a terrible notion that part of God's love consists of leaving men to decide. Even if it was up to them, most will reject it, so how unwise is that from God? But if we say he loves SOME or MANY and has actually done all to save them, and we ourselves put effort to be part of the salvation process of these people, like Paul (who knew God will not save all, but at least some, probably many) and "endured all things for the elect's sakes, that they may also obtain the salvation which is in Christ Jesus with eternal glory.", and " I am made all things to all men, that I might by all means save some." and we patiently wait for the word to take root and the elect to manifest the love of God and grace of Christ, then we are satisfied and leave the rest to the will of God.
When we limit the atonement, we only limit its extent, not its power. Because Jesus actually, utterly, and to the end has destroyed the reign of Satan, the works of the Devil, the handwriting of ordinances against us, the wrath of God and both Deaths, including the special works of Satan, pride and unbelief 2 Cor 4:4. "It is all finished" He is the author and finisher of our faith. As the scars of Jesus removed the unbelief of Thomas, his wounds, which bled 2000 years ago will remove the unbelief of the souls of those, who are sprinkled by the Holy Ghost.
Limiting the atonement isn't limiting our preaching, prayer or hope, to the contrary, who would want to stop using this power and seeing the love of God come into effect, but if we say he died for all and we are to decide, we "make the cross of none effect", or at least put a little stumblingblock to it, because we leave that last step to man, without knowing if he is honest, ready or even able to take that step. But he will be and will make it with no doubt or fear in his heart, if God has done his work in him, so we don't need to rush things and deceive people with "making a decision". God will do his will in his appointed time. As long as we sow and water, the fruit will come.