Excellent question but I think you misunderstand the doctrine somewhat. First off, Mormons do not believe that everyone goes to heaven. We believe that everyone is given a fair opportunity to choose go to heaven. The doctrine of the gospel being preached in the spirit world allows those who did not get the opportunity during their mortal lives to have that opportunity to hear and accept the gospel before the resurrection and final judgement. Those who do have that opportunity to hear in this lifetime are NOT guaranteed a second chance after death. 
 
We know that there are millions of people who were born, lived and died in areas of the world where the gospel of Christ has just never reached. Also, there were millions who were born, lived and died before Christ even came into the world. Would it be just for God to condemn these people for not accepting Christ when they've never even heard of Him? This is the purpose of this doctrine, to level the playing field and put everyone on equal terms. 
 
Now, the commandment that Christ gave to go and preach the gospel to all the world is as much for the benefit of the preacher as it is for the hearer. As we share this gospel with others, we are blessed along with those who are the recipients of the message. Participating in this work helps us develop compassion for others, increases our knowledge and understanding of the truth and brings us joy as we see the lives of others changed for the better. 
 
Hope this clarifies things for you.

The reason for Christ's Great Commission is two fold and fits perfectly into the Plan of Salvation.  
 
1) It is a commandment to test our worthiness and provide us with the opportunities to grow and learn through bringing the Gospel of Jesus Christ to the world in this dispensation.  
 
2) Remember that Christ taught Thomas that it he believed because he saw, and that it is better for those who believe in faith.  
 
Yes, Christ's atonement is universal all who are not Sons of Perdition will be give a kingdom of Glory based upon there faith and there works. Those who are Sons of Perdition and have committed the unpardonable sin of blasphemy against the Holy Ghost are sent into Outer Darkness with Lucifer and his Angels.  
 
That does not mean though that everyone who does not commit the unpardonable sin inherits eternal life though, only those who accepted the Gospel by Faith and strived to follow the commandments of God in mortality and the Spirit world inherit eternal life and gain the gift of exaltation and get to live in the presence of the Father and the Son for eternity.  
 
Those who rejected the Gospel in this life who did not have faith but accepted it in the next when they saw that the Gospel is true, they do NOT inherit eternal life. The Doctrine and Covenants is very clear on that subject. Now the real debate is about what constitute rejecting the Gospel, is it simply refusing to hear the message, is it studying the message and not accepting it, is it studying it receiving confirmation that it is true and refusing to act on that confirmation? 
 
Only Christ knows such things and only he can judge mankind on there merits and grant them there inheritance in our Father's Kingdom.  
 
Yes, Satan does want people to believe that you can wait till the next life to prepare for the Celestial Kingdom because that line of thinking is a lie that he created. Those who never heard the message of the Gospel of Jesus Christ are not penalized for this they have the opportunity to learn and commit to it in the spirit world and receive the full blessings of the Gospel.  
 
On the flip side though those that do have the opportunity to receive the gospel in this life and reject it DO NOT get a second change to obtain eternal life. Yes, they still obtain immortality through the atonement, they still obtain a terrestrial or telestial glory based upon there worthiness, through the atonement of Jesus Christ. They never obtain though the gift of eternal life which is to dwell with Heavenly Father for eternity.  
 
That is Lucifer's desire, to keep as many souls out of the Celestial Kingdom as possible, it is a pathetic mission of spite because he rebelled and lost his first estate and will never have the blessing of obtaining a physical body like we have. So since he cannot obtain a body his goal is to keep as many out of the presence of the Father forever just as he is cast out of any kingdom of glory for eternity as Perdition along with his Sons.  
 
I think that you are not seeing clearly our Doctrine which is a common occurrence. I assure you that the Church of Jesus Christ of Latter-day Saints does not believe that everyone got to Heaven or as we call it the Celestial Kingdom.  
 
Do we know who will obtain this glory and who will not, not at all only Christ is worthy of that judgement and Christ alone. He does command us though throughout the scriptures to preach the Gospel to this world , and we follow his commands and send tens of thousands of missionaries around the world to fulfill this commandment faithfully.  
 
I would suggest you look at Doctrine and Covenants 76:50-113, this is the Church's doctrinal position of the eternal disposition of the souls of mankind. As pertaining to those who died without a knowledge of the Gospel of Jesus Christ you can review section 138.  
 
It does not say everyone obtains eternal life, nor does it say that it is easy to obtain eternal life. It is very difficult to obtain this reward because much is required to obtain it. A life of sacrifice and obedience is required, a charitable heart, a meek spirit, a humble continence, and a patient demeanor. A eternity of service in the name of Jesus Christ. This is why the scriptures say that many are called but few are chosen.  
 
Heavenly Father and Jesus Christ provided a way for every single spirit to obtain eternal life should they choose to follow the celestial law required to obtain that blessing. They call every person from Adam forward to return to there presence for eternity, the problem is only few of that accept that call and are chosen to inherit the Celestial Kingdom and eternal life in the end.  
 
Of course in there benevolence Heavenly Father and Jesus Christ prepared many mansions for us based upon our merits and our faith. While we all will obtain some glory it is not the glory of eternal life, only those who are worthy and prepared for that glory obtain it.