Welcome to the forum and for having the courage to jump right in. I think there are many engines that would work in the Elio. the problem is keeping the cost down to the $6800 level. The forum has tons of information on the development of the Elio and I hope you will enjoy viewing the topic. Thanks for joining this historic journey in personal transportation.I didn't read thru the entire thread but did see some comments about using a motor already in production for the first generation Elio. I have a 2001 Honda Insight with a 1.0 three cylinder engine designed to work with a CVT or Manual transmission, auto stop, also has electric power steering. The insight engine has a timing chain, parts are readily available at any Honda dealer and the motor is rock solid with many cars reaching 300k with just normal maintenance. The down side "if any" to the Insight is the battery pack, which is not needed in the Elio.
I know Honda lost money on the Insight, but that was mostly due to the aluminum body, battery assist, batteries and extensive engineering involved in producing the most fuel efficient "Car" ever build for production. I don't know what it would take to negotiate a deal with Honda for the engine and other components but since they are now out of production a deal might be possible. Just a thought...
http://www.edmunds.com/honda/insight/2001/