I think I've found a solution, but it's painful. I signed out of iCloud on my MacBook Pro (which involved deleting data from my MBP). I then signed back into iCloud on my MBP. After a significant amount of time for iCloud to re-download data to my MBP, iBooks seems to be working correctly.
I still had to delete all of my books that were listed as zero bytes, and then re-add them from source, but this time iBooks was able to successfully upload them and I can now see them on my various iDevices.
I think that there is a bug in 10.11.4's support for iBooks/iCloud -- but it's possible that this is a remnant of the public beta (since I first connected iBooks to iCloud and upgraded my storage while still using the public beta and before iOS 9.3 was available.