- you don't understand which tag is best for the question and all the current tags on the question are not suitable,
- when some current tags on the question are not suitable and you can't find a better one
but you still think a better tag is needed, then,
- with careful consideration (analyze the question thoughtfully) create a new tag or more -- requires minimum of 300 reputation points
- the better choice: ask the veterans. Veterans may not necessarily be those only who've been with the site for a long time but can also be those who are one or more year old here but are very good and active in editing questions.
I myself tend to be in situations when I do not understand what tag is best and I do not find it good to create new tag(s) unless I'm sure there exists no other suitable tag. So I simply post the question on the site's chatroom with a brief note of the requirement and let the others take care of it.
If the user activity is low on chatroom then you can consider posting a comment on the question like:
For users: The current tags on the question doesn't properly give the hint about the question, neither the question is actually about them. But I can't think of any better tag as of now, so may be one of you can consider an edit with a better tag. Thanks!
That has been my strategy. You can find your own or may be somebody else would propose a better one.
As for the meta tags, I'm not placed at best position to comment, but I respectfully disagree with your view about them. Meta isn't a place to post anything, but it's all about the working of the main site, be it technical or user-centric issue.
If you look at your question again, you're are asking for best practices on what to be done when tags are not suitable and more....
discussion tag exactly fits the question. See its excerpt. It's meant to seek community consensus on an issue.
If you're not seeking consensus then either you've a problem in using the site which goes into support, or there is an erroneous behavior you noticed which obviously fits bug, or you want a new feature, so feature-request goes here.
Also, if you think that the current mandatory tags doesn't cover everything or most of the issues, then it's better to propose a proper and detailed use-case and then argue with why the current mandatory meta tags doesn't fit the use-case yet the use-case as a question is useful. This would give us a better picture of what's going on in your mind since I (as a normal user), as noted, doesn't find an issue with the mandatory tags. So, how would you convince the users like me?
But reserve the use-case for another question.