This may or may not be germain. After I had the battery in my iPhone 6s Plus replaced in May, Keyboard Shortcuts syncing got messed up. I had two iPads that were properly syncing to my iMac, and my iPhone and the other iPad were only syncing Keyboard Shortcuts with each other.
I spent hours on the phone with Apple support (I actually had a guy in support would call me every Friday night about 8pm and we would work on it). Eventually escalated a higher level of support but the solution was never found.
Then, 6-8 weeks ago I think it was, there must have been an attempted security breach at Apple and my AppleID got reset. It was not a password reset but some other type of reset. I had to re-enter all my info on all my devices (1-iPhone, 3-iPads, 2-Apple TV’s). It was a pain, BUT, the problem I was having went away. Since them Keyboard shortcuts are syncing properly across all devices.
So I have not investigated if the user has a way to invoke that level of reset, but that may resolve your issue.
Hope that helps, or at least made interesting reading.