To be honest, I have some other open issues here (far less complex than this one and 100% reproducible) and never get any response from anyone from plex. It’s very frustrating.
Anyway,
I faced the exact same issue today with the recent plex server and player when trying to sync 3500 music titles to The iphone of one member of the family.
What I found that worked for me is to use Plex Player 2.49 (2.50 and up is broken), and use the “old layout” (not “new plex experience” 
and obviously not the TV layout) to setup a sync. As I explained in my previous post : trying to setup from ios plex player or from plex server web player or from plex player > v2.49 fails (fail to start or not downloading). What Only worked for me is to setup a new sync from v2.49 and selecting the iPhone as the target. Then, on the iphone, kill plex player and restart it. The sync process then started and download of titles also. But the iphone has to stay on and the application has to stays in foreground to complete the download !!! Download is stoped if the app goes background or the iphone locks.
Sync is completely screwed. It’s really a painful process.
You can download v2.49 here and have a try. : Plex Media Player - #94 by pcalves
EDIT : I just synced 3800 music titles like this. And it “almost” worked. Some side notes : to avoid the sync and download process to stop when application goes background or the phone locks you can play in plex - on the phone - a title in loop during the initial sync, it will keep the app active in foreground. My fist sync was stuck @99%. On title left to be transferred but no more conversion or download activity on the server side. I found that 1 title was making the converter to hang/crash and all the sync was stuck. There is no indication of what data has not been transferred, you have to manually scroll all titles to find out which one is “not synced”. Once again, painful and error prone.
