Georgette,
If you delete them from the PDF folder, it will delete them from iBooks. What I found is if I moved them from the PDF folder, as if they were new files, to a collection, then I could organise that collection and it would remain in the order I had imposed. The newly moved item(s) got shunted to the top of the PDF folder shelves, but as I don't use that folder then I wasn't too bothered about the organisational mess that it is.
What happened initially when upgrading iBooks is that all my PDFs got resynced back to my iPad and, despite appearing as before in the different collections I had made, they would not stay in any type of order. Hence the reason I deliberately moved them again from the PDF folder on iPad, to confirm where I wanted them to be, and then I was able to organise my shelves and they would stay put. But in addition they still appeared in the PDF folder. I don't know if this is what is technically happening, but the PDFs we see in our personal collections in iBooks act as if they are just a short-cut icon to where the files really reside - in the PDF folder. So deleting them from that folder truly deletes them from iBooks.
Perhaps to meet your needs you need to forget using the system PDF folder as a repository for knowing what PDFs you have read, or have to read. Just create a folder, for example, for New Reports, move any new PDFs to that collection and then transfer them out once read. Unfortunately it will take a while to deal with all the existing PDFs in your iBooks - identifying which have been read or not. But once that is done, my experience is that my collections are now stable and are acting as they were before the upgrade, apart from the new behaviour of the PDF folder.
S