If you those Page layouts are created as user presets then, they can be manually transferred over.
You need to look for those presets at the below location and transfer them to the same location on the other machine.
Mac : /Users/[user name]/Library/Application Support/Adobe/Lightroom/[preset or template folder]/[preset or template filename.lrtemplate]
Windows : C:\Users\[user name]\AppData\Roaming\Adobe\Lightroom\[preset or template folder]\[preset or template filename.lrtemplate]
I think this works- Well it did for me!
Open a Book from your 'Saved Book" in the Collection panel (This is not a 'Standard Collection' )
Right-click on the "Book Collection" in the Collections panel.
Choose [Export this Collection as a Catalog]
Include 'Negative Files' (if not on other computer)
Include 'Available Previews'
Save your 'exported' catalog to a USB stick.
(Test it by Opening the 'exported' catalog (.LRCAT) on another computer with Lightroom.)
I opened a book, did the Export as Catalog (with Smart Previews only), to a desktop folder, and I could open it as a new catalog with all my page designs intact. (screen clip from my 'export' catalog book)
And the last step would be to "Import from another catalog" (the USB) into your master catalog on the 'other' computer.
This is the answer I'd have given. It's a workaround, but it does work. Using Export carries everything from the catalog, keywords, collections, as well as saved books, web galleries etc. It doesn't bring Publish Services collections though. Nice one!