Have you looked at the Reading List plugin? It is intended for this. You create a reading list for each list and put the books in them. The list maintains the order of the books in them. The list can also set a column value as the book is added or removed. That could be a tag-like column with the list name for searching. You won't see the order in the list in the library, but, you also don't need a multitude of extra columns to account for the number of lists you want.
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