That is an EXCELLENT analysis and solution. I was seeing a similar problem on our new Dell 5767 after migrating the system disk to a Samsung EVO 500GB SSD using the EaseUS Todo backup "free" clone software. It turned out that partition 1 had a totally garbage label. This was causing Retrospect backups to fail when they tried to invoke the ASR writer to save the system state. GPT fdisk worked flawlessly, especially since you had honed in on the specific commands that were needed to apply valid labels to all of the disk partitions.
I have no idea why Microsoft's DISKPART tool is apparently unable to either display or fix partition labels. Since having valid labels on both the disk volumes AND ON THE PARTITIONS is critical for system stability, you would think the supported tools would be able to check them and fix them as needed. They don't.
It's worrisome that the EaseUS cloning tools generate garbage partition labels, especially since it can break critical parts of the Windows and third-party backup solutions. I can't imagine they do it to force people to use their software to be able to do "bare metal" system recovery.
DrTom