After plenty of experimentation, this is what worked for us.
How to Mount Synology NFS Share on Proxmox Backup Server
Synology DSM 6.2.4-25556 Update 3, with BTRFS volume (required) [1.2.3.4]
Proxmox Backup Server 2.1-1 [1.2.3.5]
On Synology [1.2.3.4]:
1. Create Shared Folder 'xxxx' on a BTRFS Volume (volume1 in this case), and give 'admin' Read/Write permission.
2. NFS Permissions tab: Privilege: Read/Write, Squash: No mapping, Security: sys, Enabled Async (checked), Allow Connections (unchecked), Allow Subfolders (checked).
On PBS [1.2.3.5]:
3. Create and Mount 'xxxx'
mkdir /mnt/xxxx
mount 1.2.3.4:/volume1/xxxx /mnt/xxxx
4. Add Datastore 'xxxx' using Backing path: /mnt/xxxx
5. Open/Refresh Datastore page (you should see Error 13 on 'xxxx')
6. Umount 'xxxx'
umount /mnt/xxxx
On Synology:
7. Open Shared Folder 'xxxx', NFS Permissions, and change Squash: Map all users to admin
8. Browse to 'xxxx' and Delete '.lock' file
On PBS:
9. Remount 'xxxx'
mount 1.2.3.4:/volume1/xxxx /mnt/xxxx
10. Open/Refresh Datastore page (Error 13 should clear)
11. Perform host backup on a Proxmox Node to verify (e.g., /etc folder which is usually small). This assumes you've already connected Node to PBS (add Cluster Storage PBS Server).
proxmox-backup-client backup nodeABC-etc.pxar:/etc --repository 1.2.3.5:xxxx
Notes
I suspect this process highlights a bug in PBS datastore creation. It requires 'backup' uid/gid 34:34 to create the .chunks folders, but seems to prefer root after creation (for UI and client backups). It wasn't necessary to create a 'backup' user on Synology; that just led to uid/gid headaches.