The phrase "and ever more efficiently" is correct and usable in written English.
It can be used to describe an ongoing improvement in efficiency over time.
Example: "Our team is committed to finding ways to work smarter, and ever more efficiently, to meet our goals."
Alternatives: "and increasingly efficiently" or "and more efficiently over time".
"Working with communities and stakeholders ever more efficiently, we will assess challenges and implement solutions on a 'landscape scale', always focussing on the ultimate outcome: an improved environment for all of us".
New wells are beginning to be drilled with break even at prices as low as $35 a barrel, as companies learn to explore and produce ever more efficiently.
For the time being, we have a fossil fuel glut, as the technology of extracting hydrocarbons has put supply ahead of demand and the need for energy services — miles driven or flown, newspaper articles fetched to a screen, and buildings heated and cooled — is being met ever more efficiently.
Now, the city's true poor are hardly visible, and the middle classes squeezed ever more efficiently out of sight.
FHM WroTheseGuide to the Internet 20 Years Ago and It's Hilarious.
China's censorship machine has been operating ever more efficiently since mid-2008, and restrictions once viewed as temporary — like bans on Facebook, YouTube and Twitter — are now considered permanent.
Most economists remain confident that the conventional analysis of the population problem is substantially correct: a steady flow of new technology that uses resources ever more efficiently will offset any scarcity of minerals and arable land, at the very least dampening the tendency for commodity prices to rise.
The new biosynthesis routes 'tap' the metabolism ever more efficiently, particularly through the engineering of driving forces and utilization of cofactors generated during the light reactions of photosynthesis, resulting in higher product titers.
