I see. Well, im not sure that logic is sound. I can make a claim that someone existed, for contrast lets say someone we know is fictional like Harry Potter, based on face to face interaction and you can claim to have had face to face interaction with me and a third party can have claimed to have had face to face interaction with you. If I then corroborate the third party historically, and you and then me but fall flat corroborating the historic existence of Harry Potter, then we have good reason to be rather skeptical of Harry Potters historical existence. The chain of direct association is maintained precisely as in your example but we wouldn't see that as making the claim of Harry Potters historical existence. I dont think direct association makes a significant difference, though I suppose it would depend on the nature of the references.
I agree completely that it doesnt matter when considering the works themselves. The wisdom doesnt go away. As you say, we need not know the author at all to learn from the book.

Im not sure what you mean...
There is substantial, overwhelming even, evidence that Alexander the Great existed. It is corroborated by a mountain of historicity.
There is quite a bit less for the existence of Plato, but still a very comfortable amount for acceptable historical acceptance. (For historians at least )
Socrates is still another large degree more lacking in corroborating evidence, which has led to some doubt as to whether he existed at all by historians.
I share your concerns about Platos works surviving intact, but could you elaborate on “by direct association”? You may be referencing historical corroboration im not familiar with.

In the interests of strengthening your argument, I offer these criticisms.
I think you make a mistake right out of the gate with 1., which I take to be the premiss of your argument. Surely you would concede that there are things which exist but are not in the bible? Like black holes and many varieties of living creatures, hell could exist as well. This seems to dispell your premiss entirely.
I think 2 would be stronger if you made a distinction between differing states of existing, rather than restricting existence to exclude purely mental phenomenon. It is clear that things that exist conceptually still exist, so 2. will serve objections to your arguments if you structure it the way you have.
3. Is a pretty safe claim as far as I can see. There may be some wriggle room for interpreting the bible as alluding to a hell, but you seem to have largely countered this with some of your preamble before you stated your argument itself. (By defining hell specifically). You might want to include that as part of your argument structure somewhere.
Your conclusion in 4. doesnt follow from 1. In my opinion. I think what your argument accomplishes is concluding something like:
4. Therefore, concluding that hell exists based on a purely biblical account is not a reasonable conclusion.
I think you would still have some work to do if you want to make an overall religious argument against the existence of hell, there are biblical basis for accepting claims of hell existing from the clergy or in non-biblical religious texts and you would have to address those as far as I can tell.

I dont know about that, there is more evidence Plato actually existed than there is for Socrates. Of course, Im fairly skeptical about the accounts of anyone in ancient history. Even a mere 200 year old account is dubious in my books, as far as an accurate account of the person in question.

To the OP:
It is possible for someone to believe in a god, and believe morality can only come from god, and still believe in secularism. Secularism is not the belief there is no god, it is the belief that ones god beliefs should not be used to determine the way our society should operate. This seperation of church and state is very wise even if you hold religious beliefs, becuase other people hold other, different religious beliefs and in order for everyone to be able to get along fairly and equally with a society or culture it makes sense to set aside personal religious beliefs for such governance. You dont get to force anyone to live by your religious beliefs, but neither can anyone force you to do so.
This is a perfectly sensible thing to do, even if you think your own morality is divinely inspired/based.
So I cannot help but disagree.