[LilaFrabel]

Hi, I'm organizing my tags too and I think Categories may be the solution for you. Like you said there are different types of tags so why don't you split them to keep them more organized? You will not still be able to organize in the order you want but if you don't create too many categories you will be able to keep them always in sight in the tag browser.
The only drag is that every time you create a tag, you must add it in his own category (and this become a litlle more complicate if it's on more categories), even if it's a child of a hierarchical tag that already exist in that category. This system works until the tags are not changing too often.
Other than that I think that Categories are underrated, but worthy, give them a try!