What about swapping in a VW TDI engine.
Acme Adapters makes an adapter to attach the TDI to a Toyota 5-sp manual trans.
https://www.acmeadapters.com

Or a 30HP kubota, and a gearbox with wide spaced gears and an overdrive, so you've basically got 8 or 10 ratios to play with.

I bought a Miata last weekend, and I've noticed that the gearing is very low (as in high rpms). At 40mph in 4th gear you're already spinning at 2500+. I think the best gas mileage bonus would come from a 6th gear or a regeared differential (which may or may not be possible)

I know a guy that put an S2000 engine in his Miata. Besides custom engine mounts, swapping over all the wiring, defeating the Immobilizer, and swapping over the cluster, he had to have a custom driveshaft made. Then he had to ship it to the east coast to have this place balance it for him. But the answer is that if you have to ask this question; you can't do it.

I don't think it would be more efficient than the Miata engine.

The basic answer I have found to "Can X engine go in Y car?" is yes. The only factors are time, money, and mad skills dealing with fabrication. I've seen (not in person but magazines, forums, etc) a Viper powered Pt cruiser, 351 Winsor Focus, VTEC original Mini, Twin engine 1st gen CRX, V6-mid-engined 3rd Gen Civic Hatch, S2000 powered 318i BMW, even a rocket powered 2nd Gen CRX to name a few. The possibility is always there, the rest is up to you and your resource limits. Mak

I see no reason why the Civic engine spinning the way it does creating an issue if you used the Civic transmission. Why would something like that matter?

Civics are front wheel drive, using a transverse mounted engine and transaxle. Miatas are rear wheel drive using a longitudinally mounted engine mated to a typical transmission, drive shaft and rear differential. A Civic transmission cannot be easily used to drive the rear wheels (well, unless you put the engine and transmission in the trunk), so an adapter plate must be used to allow the Civic engine to mate up to a rear wheel drive transmission.