Change the way the parent book is selected

You write that you were inspired by the Menu Link Weight module to create this module. Menu Link Weight module has an integration with the Client-side Hierarchical Select module, which simplifies the selection of the parent menu item.
We have a very branched hierarchy of books on our site. The creation of new child pages does not cause problems - went to the desired section, clicked "add child page" and you're done. But very often there are situations when it is necessary to move a section of a book to another parent section, for example, if it was mistakenly placed in the wrong section, or, for example, when information that has lost its relevance needs to be moved to an "archive" section. The posting of information on the site is mainly done by elderly people who cannot be entrusted with administrator rights, since they can accidentally spoil something. Therefore, for editing the hierarchy of books, they only have access to a standard user interface, which is extremely inconvenient when a book has a huge number of sections and subsections, like ours - to select a parent section, a drop-down list with a full tree of the entire book is used, where the section names are often abbreviated to 2-3 words, which makes the choice extremely difficult.
http://new.partizansk.org/sites/default/files/adverts/2021_02/111.png
As you can see in the screenshot, often different sections in this drop-down list are labeled the same. The integration of the MenuLink Weight module with CSHS makes it much easier to select a parent menu item, which has the same standard user interface as books - a drop-down list with a full tree of menu items - thanks to the CSHS integration, each menu level is selected in a separate small list, which is much convenient.
http://new.partizansk.org/sites/default/files/adverts/2021_02/222.png
Here's what would be much more convenient to select the parent book

(I'm sorry - i don't khow how to insert screenshots correctly)