The root cause of the issue was that the six problem VMs were created in the format ".xx VM-Name" with a period and the IP address at the beginning of the name. This in turn put the leading period at the beginning of the folder name and all files created for the VM. Putting a period at the beginning of the file/folder name caused the files to be hidden in the ESXi file system, which was causing the issue. The VMs that were replicating successfully had been created without the period at the beginning of the name, but had been renamed afterward to that format. The easiest way to fix this would have been to shut off the VMs and clone them, but I had some space limitations on the SAN in question, and it would have taken a lot longer to clone than rename files. I ended up having to remove the VMs from inventory on the source vCenter, remove the period from the folder name using the datastore browser, use SSH to rename the files in the VM folder with the command (mv ".xx VM-Name.yyy" "xx VM-Name.yyy") (use ls -a to see hidden files), use WINSCP to download the .vmx, .vmxf, .vmdk files and manually edit them to remove the references to path/filename with the period at the beginning, then uploaded the files back into the folder. Granted this is a little more risky than cloning, but I was kind of forced to go this route. I imported the VMs back into inventory, removed the old VMs from the Veeam jobs and added the new ones, mapped my backups and replicas, and kicked off my jobs. The backups and replications had to recalculate the disk digests again, which took a long time due to some of the VM sizes, but both backups and replications completed successfully.
Lesson to take away from this: don't start a VM name with a period.