Rated 5 out of 5 stars

Two fans thank you. My laptop's for an extended life and myself for the Sound of Silence ;-)
Two suggestions then ...
1) Pause/Resume Window (all tabs within) for those who organize them by subject
(Maybe Shift+Pause Shift+Resume to avoid invading the menu space)
2) A third status in addition to Paused/Resumed : Automatic.
It means that the tab
- is like resumed when it "gets focus" (starts displaying (even partially is best, if possible))
- is like paused when it looses focus (gets hidden)
At first sight, everybody should prefer Automatic unless they want to listen to muffled background music or use transparent windows to watch the video that's behind.
Seriously, it's a rare thing but there can be a process "running" in a background window or a window can "underlap" waiting for something to be dropped on the visible part.
The best of course would be to just prevent the tabs receiving CPU slices unless they have to refresh the display. That would make the display visible immediately. If no CPU is allowed, the memory is not accessed and the real memory is paged out to be used by other processes.
A >3.7a4pre version is a great idea too !!! In the name of 2,635 users, "yes please".
Encore merci.