Very cool of you to take this on, Nate. I don’t have the need for it myself, but I was excited to try it out. It works great!
I do see a gotcha, though, when there are multiple tags on a topic. (And it’s hard to imagine managing things with only one tag per topic.)
Tags are either sorted alphabetically or by popularity…
…so the author has no direct control over which tag shows first.
I thought using a non-alpha character to start the client tags (~ClientName) might always pop it to the head of the list. This works on the /tags page – but not on a topic, where the tag list just ignores the ~ character. 
In a topic from last year, it appears that certain non-alpha characters could be inserted invisibly to force sorting: Invisible way to force display order of tags? but it seems this doesn’t work now. When I create a tag today with an apostrophe or comma it’s either rejected or silently stripped out. (Not sure why ~ is accepted.)
The tag sort setting shown above affects both the /tags page and the tag list on topics – but I guess they must use a different alpha algorithm?