If you were happy with the subs for games and movies via the AVR before, I personally don't see the need to route the sub outputs through the flex. If you do, you will have to use the flex at a set level when using analogue in and use the flex to control the volume when listening to music, there is no way around it.
The way you describe wouldn't allow you to adjust the volume when listening to music and keep the l+r outputs at the same level as the subs, as if you turn the volume up or down on the 6000a the subs volume won't change and will be too high or low (relative to your mains).
Personally, I would just leave the AVR to manage the subs for movies/games and play about with Audyssey app to tweak them if you're not happy with games/movies.
Initially the intention was to integrate the subs better for stereo.
Adding a 2x4hd wouldn't solve it, as far as I can see, and would be a lot more complicated (and as you say, more expensive) than just setting the flex to a given level for movies.