Before the dead saints are raised from the dead they will not have any body, because the body they had will have returned to the dust it was made from.
Because they will not have any body, they will have no soul.
When people they die, they are no more, they do not exist, they are gone.
The only thing left of the dead saints before the resurrection will be the dust that used to be a body and the life force that returned to God upon their death.
The dead saints will have a newly recreated soul with a new immortal body in the resurrection.
I'm not sure I'm quite as content as you are to believe that there is nothing left of the person that dies. What that thing is that is left is up for some discussion.
Here's a suggestion--memory. We can keep a computer "alive" by switching hard drives. The rest of the machine (the "body") can be completely replaced (or "upgraded", perhaps?), and the power source (spirit?) can be removed and replaced as needed. I'd probably put the operating system in the same category as the hardware components.
But the whole purpose of the computer is the stuff that it was meant to create or manipulate or hold on to, such as spreadsheets of business transactions or pictures or contact information, etc.
When we get a new computer, we transfer all of that stuff to the new one.
I don't know how God would retain that memory, but I can certainly imagine He has a way to do it, even if only in His mind.
If the body that is resurrected has some connection to the body that died, then there would also be a memory of that, I suppose. DNA is one proposed memory device for that part of it. So even if a body has been incinerated, God would be able to reproduce it out of incorruptible materials. That would make most resurrected bodies different from Jesus' resurrected body--His did not undergo corruption, and that might be why He still retained His scars of the crucifixion.
When we are all "changed in the twinkling of an eye", I can imagine that whatever defects there might be in our physical bodies (loss of limbs, genetic diseases, acne, whatever) could be corrected, although the passage about it being better to enter into the kingdom without eye or hand is intriguing. (Mat 5:29-30)