The previous two posts touch on the same notion.
We may be getting somewhere.
An old biblical story forms a situation where a man having gone to hell,
is close enough to the angelic to have conversation with one of them.
Never have I heard anyone notice and then report the perspective.
If you can be close enough to have speech with the angelic...but they say...
'....there is a great divide between us....'
then being without heaven is possible....no matter where you stand.
Error sent that one character to hell.
Yet, he can speak to the angelic.
Sin may very well be used to say...'without'.
I would say that you could certainly use the term "sin" as meaning "without." I had come to the same conclusion as you about taking the meaning from the Spanish word and had applied that concept for a number of years prior to the Greek meaning and origin being mentioned to me about 5 years ago. In applying the concept of "without" it did give me a better understanding than the "stain on the soul" concept that did not make any sense for me, and that I ultimately found to be inadequate.
However, I also found that the "without" meaning did have some limitation in application, because if God exists everywhere we really can't be "without" him -- but we can suffer from an illusion that we are without him. It is valid for the purpose of describe a state of being we may call "Hell."
I would rather use a more accurate definition than a different one I might prefer. It just so happened that when a new meaning for the word was presented to me, and I looked it up myself, then I applied it in my understanding -- I found that not only did things in the Bible make more sense for me, it also shifted many Bible stories, especially those featuring Jesus, into a much gentler and kinder understanding.
For example, it changes: Go, and sin no more
From: Go, and don't be without God (or god-less) any more (which seems like a judgement of the person)
To: Go, and don't make that error any more (now that you know better, apply that wisdom in the future)
I don't wish to convince you that you ought to change your definition. I am just stating what I have found to be the benefit of applying a definition that I understand to be more accurate to the original meaning, in case it is of benefit for you.