The problem is almost certainly in the never-to-be-damned-enough Android Storage Protection Framework that CC must use to access an SD card in Android version 5 and later. The SPF can be very very slow.
I assume that you verified that the folder structure on the SD card matches your template. It is easy in calibre to think you are using template A when you are in fact using template B.
In your case, my guess is that you are running into exactly the problem described in the
FAQ you referenced. The SPF gets more and more slow as you add more book files to a single folder. The way to avoid the slowness is to minimize the number of files in a folder. Using your template, all books without a category and without a series are stored in the {tag} folder. That can be a lot of files.
Solution 1 in the FAQ
How do I get the same file names in CC no matter which connection I use? tells you how to enter a CC template.
If you really want to have the {tags}/{#category}/{series}/ in the file name (when using CC, file names aren't very important) then you could try this CC template:
Code:
{tags}/{#category}/{series}/{first_author:%1.1s}/{first_author}/{title}
This template avoids the problem described above (no category and no series) by adding folders based on the author name.