"Are [those barred from Communion] also barred from Heaven or is it just used as a stigma like a big red "A" on their foreheads?"
No, they are not barred from Heaven (only God is a just judge on this); nor is it supposed to be a big red "A" on their foreheads. In fact, it needn't be known to any but themselves.
That "needn't be known" is a little difficult when, as is the very loose custom now, practically everybody --- including the scandalous Pelosi--- goes up for Communion whether they were well disposed spiritually or not. The optics are like a Chinese Fire Drill, and those who don't go can look visually isolated. I know that when I have judged myself unprepared for Communion (e.g. because I violated even the very nominal "fast") I have felt a tiny twinge as if somebody might notice and think, "What's with her? Is she in mortal sin?"
This is mitigated in parishes where people (even non-Christians) can get in the communion line and ask the priest for a blessing, rather than receive the Sacred Host. But as I understand it, not all parishes do it that way.
So why are the divorced-and-remarried turned away from Communion? For the simple reason that they have, by remarriage, publicly proclaimed that they are involved in an ongoing sexual union with a person not their spouse (the new "marital partner") which Jesus called, three different times, adultery (Matthew 19:9; Mark 10:11-122; Luke 16:18). Painful word. I didn't make that up, and no hierarch of the Catholic made that up. That is Christ's word,He used it repeatedly, and dang it all, we're stuck with it.
So to give people Communion when they're in an ongoing relation of sin, does severe harm in three ways:
(1 Cor 11:27-29) "So whoever eats the bread or drinks the cup of the Lord in an unworthy manner, shall be guilty of the body and the blood of the Lord.
But let a man examine himself, and so let him eat of the bread, and drink of the cup.
For he that eats and drinks, eat and drink condemnation unto himself, if he discern not the body."
So good pastoral care of the divorced-remarried couple, should include protecting them from bringing this curse upon themselves.
By the way, giving Communion to public, overt, unrepentant abortion-promoters and gay-marriage-promoters like Pelosi, Cuomo, and the rest of the apostate-Catholics, sends exactly the same message, and is horribly wrong for exactly the same reasons.
"Funny how mortal men can decide to "annul" a marriage..."
Well, would it be better for people to be trapped in a marriage which never was a marriage to begin with, because of some defect that rendered it void? What if a man married a woman and then found out "she" was a tranny? What if a woman married a man who deceived her and never intended an exclusive, faithful, lifelong marriage from the git-go? What if this was a very young couple, pushed into marriage via bribes and threats from their parents?
Those would not have been valid marriages to begin with: it is simple justice that there must be a tribunal which would examine the evidence, make the determination that there was no bond, and free the two to go forward with their lives not burdened with a false union.
"... but claim that God can't be communed with by those who haven't had the experience doled out to them by some other flawed person (we are all flawed from the basest criminal to the highest Pope). "
It's not a question, broadly speaking, of who can "commune" with God. Any sinner can make fruitful contact with God with every prayer of true contrition. If a person in a situation of mortal sin wants to "commune" sacramentally, the way to do it is to go to Confession --- that's the sacrament for them ---and from that time forward, abstain from adulterous acts.
I hope this explanation helps. If you have further questions, or even objections, please go ahead and ask me again.
Mark 10 states it this way: 10 When they were in the house again, the disciples asked Jesus about this. 11 He answered, Anyone who divorces his wife and marries another woman commits adultery against her. 12 And if she divorces her husband and marries another man, she commits adultery.
Is that the true stipulation - that the one who actually does the divorcing is the one committing adultery?
Luke is the only one who expanded the explanation, but one must consider it to be true.
Last question for this topic. How is adultery different than breaking any of the other commandments while living under the New Covenant? Jesus died for all our sins, past/present/future. God told us that when He made the New Covenant, He would: "...forgive your wickedness and recognize your sins no more". Why, if one can "prepare himself for Communion by going to Confession and repenting, even though he will be committing the same sins tomorrow and the next day, etc., why can one who is divorced and remarried also confess, do the prescribed rosaries, and receive Communion?
Thanks again for your penchant for politeness and patience when helping to explain my questions/sense of confliction with my personal beliefs.