I am convinced that your interpretation of the Bible on the subject of eternal punishment is correct. I am fully aware of some of the explanations offered above that seek to mitigate the notion of eternal suffering. I have long believed that they are wrong.
Having said that, I wonder how someone who believes as you do can explain how a God of love and mercy, supposedly, can take a “good” person, ignorant of Christ, and make them suffer forever.
If a parent spanks a child, we like to think it is motivated by love and concern for the child. If they spank a child for an ten minutes, we’d say that was excessive. If they continued to wail away on a kid’s butt for an hour, we’d say they are monsters. And yet a God “spanks” billions of people forever and ever without end, and yet we claim He is loving and merciful. I wish someone would explain that to me.
For example, Romans chapter 10 presents the idea that the whole world has heard the Gospel - at least in Paul's day. Here's the pertinent verse:
"But I say, Have they not heard? Yes verily, their sound went into all the earth, and their words unto the ends of the world." (Romans 10:18)
One shouldn't make a major doctrine from one (relatively obscure) verse. But the language is that the whole world heard the Gospel message, at least at one time.
Then there is the idea that God can be known by creation, it's given statement in Romans 1:
"For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who hold the truth in unrighteousness; Because that which may be known of God is manifest in them; for God hath shewed it unto them. For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse: Because that, when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened. Professing themselves to be wise, they became fools, And changed the glory of the uncorruptible God into an image made like to corruptible man, and to birds, and fourfooted beasts, and creeping things." (Romans 1:18-23)
That makes it pretty plain, God "shewed" it, it is "clearly seen", "without excuse", "they knew God". That kind of language doesn't leave many options.
Then you have John 3, the words of Jesus Himself:
"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. For God sent not his Son into the world to condemn the world; but that the world through him might be saved. He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God. And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil." (John 3:16-19)
"light is come into the world", and men love darkness instead.
It is very difficult to imagine that God somehow doesn't have the ability to make the Gospel known, or that He hasn't. But the fact remains that humanity is alienated from God because of sin. Jesus made reconciliation. The condemnation is because of rejecting Jesus.
There is also the teaching of "election" in the Bible. It shouldn't be confused with "predestination". It is plainly stated an number of times. On the other hand, never do we find any statement of "election to depravity". That is (IMHO) merely a human need for symmetry of doctrine. God's word doesn't seem to have the same need.
As far as "good" people go, there isn't any such thing. Romans 3:23:
"For all have sinned, and come short of the glory of God;" (Romans 3:23)
I'd suggest reading the entire of chapter 3 in Romans.
Anyway, the idea that somebody ignorant of Christ is condemned for that ignorance - well that's a toughie. Old timers used to say that if we're so concerned about those who've never heard we ought to rush out and tell them.
The Bible only says that Christ is our savior, and there is none other name under Heaven by which we must be saved. As far as those who haven't heard, I don't think we should make doctrines where the Scriptures are silent. But we have plenty of warrant to teach the only basis of salvation.