Lord_Dweedle, a good and difficult question to answer in the light of available knowledge derived from ancient holy/religious scripture available to us today.
First of all, I myself am an Agnostic and have had my fair share of studying of religious scriptures. I have moments that I think God exists, on the other hand I realise that this physical world is so absent of a God-like metaphysical being that I sometimes hold another e.g. evolutionary answer to our existence to be true, and on the other hand again I regularly have the tendency to just keep it, yes an Agnostic mystery, something we can't really get an answer to. Maybe more towards a Buddhist tendency.
But since your question deals only with `God and Heaven-Hell´, we must see it in that light - trying to find out if there is a God that does exactly NOT that; sending good people to Hell just because they don't believe he exists? As many do, I would also like to give my own opinion on this matter, however since our knowledge/understanding of the concept of God has been derived from scripture, at this point it makes more sense to try and find valuable answers in there.
I will now quote various sayings that I like from an otherwise orthodox questionable believe system on various fronts. This could maybe make us ponder more on how (orthodox) religions may have it interpreted correctly or not, or how any believe system (stemming from your own mind even) interper God's (if he exists) "kindness" to us, as that is what it comes down to eventually. Is God kind/forgiving/merciful, etc. enough to send certain people to a good place, and is it one way or the other justifiable (whether Heaven or Hell)? Honestly, I too still have big question-marks about this, as so many other people rightfully believe, it's Ungodly, even Unhumane, to send any substantially good person, or even somewhat bad person, to eternal hell and damnation, no matter what they believe. This, I agree, in particularly today's day and age, is a very narrow-minded view of the world, and I doubt this is what the God that may perhaps exist has intended.
As I mentioned before below quotes originate from a currently orthodox religion, maybe you can tell by the end which one, however I want to take these sayings on face value trying to understand God's nature through available sources that deal with the specific God subject, so we could look at things in a different way (as that's the essence of the initial question of this thread). I find them interesting and taking a good look at various of these quotes, I could say that Jeff in your example, has a good change of being pardonned by this God, and going to heaven, because he was a substantially good person (even though he didn't consciously believe in Him).
Read the quotes first please, then we can ponder upon them and the possible part of it in the larger scheme:
There is a reward for kindness to every living animal or human.
Even as the fingers of the two hands are equal, so are human beings equal to one another. No one has any right, nor any preference to claim over another. You are brothers (& sisters).
All doings are built on intentions, and every man will be rewarded or punished (for his work) according to his intention
All mankind is from a single source, a white man has no superiority over a black man nor a black man has any superiority over a white man except by piety and good action.
Do not turn away a poor man...even if all you can give is a little bit to spend. If you love the poor and bring them near you...God will bring you near Him.
God does not judge you according to your bodies and appearances, but He looks into your hearts and observes your deeds.
The person who looks after an orphan and provides for him, will be in Paradise.
It is better for a leader to make a mistake in forgiving than to make a mistake in punishing.
It is better for any of you to carry a load of firewood on his own back than to beg from someone else.
People, beware of injustice, for injustice shall be darkness on the Day of Judgment.
Righteousness is good morality, and wrongdoing is that which wavers in your soul and which you dislike people finding out about.
The best among you are those who are best to their wives.
A woman was punished because she had kept a cat tied until it died, and (as a punishment of this offence) she was thrown into Hell. She had not provided it with food or drink, and had not freed her so that she could eat the insects of the earth.
(Each one) of you should save himself from the fire by giving even the smallest of charity. And if you do not find a just cause, then (by saying) a pleasant word to your fellow beings.
A prostitute was forgiven by God, because, passing by a panting dog near a well and seeing that the dog was about to die of thirst, she took off her shoe, and tying it with her head-cover she drew out some water for it.
While a man was walking along a road, he became very thirsty and found a well. He lowered himself into the well, drank, and came out. Then [he saw] a dog protruding its tongue out with thirst. The man said: "This dog has become exhausted from thirst in the same way as I." He lowered himself into the well again and filled his shoe with water. He gave the dog some water to drink. He thanked God, and [his sins were] forgiven. The Prophet was then asked: "Is there a reward for us in our animals?" He said: "There is a reward in every living thing."
He said, "The deeds of anyone of you will not save you (from the fire [of hell])." They asked, "Even you (will not be saved by your deeds), O God's Apostle?" He said, "No, even I (will not be saved) unless and until God bestows His mercy on me. Therefore, do good deeds properly, sincerely and moderately, and worship, and always adopt a middle, moderate, regular course whereby you will reach your target (Paradise).
You should adopt humility. So that no one may wrong another and no one may be disdainful and haughty towards another."
God will not be merciful to those who are not merciful to people
Avoid cruelty and injustice for, on the Day of Judgment, the same will turn into several darknesses; and guard yourselves against miserliness; for this has ruined nations who lived before you.
Seven kinds of people will be sheltered under the shade of God on the Day of Judgment...They are: a just ruler, a young man who passed his youth in the worship and service of God...one whose heart is attached to the mosque...two people who love each other for the sake of God...a man who is invited to sin...but declines, saying 'I fear God'...one who spends his charity in secret, without making a show... (e.g. this could be Jeff?) and one who remembers God in solitude so that his eyes overflow.
