Is it possible to reorder tables in phpMyAdmin?
Not exactly, but you might be able to improve things regardless.

For instance, in a database structure tab, you can sort based on any of the columns; table name, row count, collation, etc. In your specific example, you could simply sort the tables in reverse order (by clicking the "Table" header to invert the default sort order), though of course that isn't a universal solution.

From the navigation frame, you can use the favorite tables feature (which puts selected tables in a quick-access dropdown menu), the show/hide tables feature to hide tables you rarely access (sounds like you're already doing this), and the filter dropdown to quickly find and access an arbitrary table by typing a few keystrokes.

I don't it's not really a complete solution to re-ordering the display of tables, but at the moment those are probably the best solutions available.

As a side note, this would make an interesting feature request for the project issue tracker.