I'd be generous and make it 3d4 for each round of its effect, including all the extended rounds.
After all, if someone used empowered, extended sleep, I wouldn't make the creatures additionally slept by the empowerment wake up before the extended duration started.
If you empower and enlarge a cone of cold, does the whole cone do the extra damage?
Silly examples, but do you get my point?
The non-stacking of maximise and empower is obviously the touchstone when trying to think about how metamagic stacks, since that example is clearly given. I think it makes sense when looking at metamagic which affects the same component of the spell (they both affect damage). When the metamagic affects different components (damage/range/duration) I think it is simplest to allow them to fully improve one another. After all, in the example above the empowered extended Acid Arrow is a 5th level spell... and even with my ruling is nowhere near as powerful as Cone of Cold or Cloudkill...
Cheers