For many years my students' and my personal absolute favorite class III mallet solo (2 mallets) was always:
Petite Mallet Suite
It's not in a book though. It's a single solo. It has 5 contrasting short movements that are fabulous in my opinion. Several times I even had a group of my percussionists (middle school) perform it in the spring concert as a group while I played the piano accompaniment.
I still have an MP3 recording I made of the score and mallet part I scanned into PhotoScore and imported into Sibelius to create a sound file years ago if you want to hear what it sounds like, keeping in mind the recording is only digitally generated.
Here's the link on my Google Drive if you (or anyone else for that matter) want to hear and/or download it: https://drive.google.com/open?id=0B8AarMD-ON-OMkRsMmo4VTlkRW8
Recommendations for a very accessible and enjoyable class III mallet solo (2 mallets)?
If you make a suggestion out of the Southern Special book, and you would be willing to share a scanned copy, it would be awesome. I have the book, but it is currently quarantined with the rest of my library until whenever... hopefully before Christmas.
I will order others. I just don't want to spend money on a book I already have.