Virtual Libraries(VLs) based on 'marked' searches aren't going to be reliable because the 'marks' on books aren't saved. They're meant to be temporary.
The Reading List(RL) PI keeps the id's for the books in each list in its own configuration. When you view a list, it sets a 'marked' value on each book in the list and then searches for that mark. Those marks are cleared when you next do something else that marks books.
For VL searches, I suggest you use column values.
RL can populate custom column(s) for you, so you could make a custom column (tag type probably) specifically for your lists and populate a value for each list, then use that for the VL searches.
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