I have found The Great Suspender (Chrome Store, GitHub) to be a really useful extension for managing my 'sea of tabs', when I haven't yet got around to 'sleeping' them all.
It could be useful to be able to suspend/unsuspend tabs to the left/right/in this window/etc.
As per my ponderings in #6 (RE: implement new features vs tighter integration with other extensions), this is left open as a future potential pondering.