I sat down and went through the references you supplied. Also some of the internal references in those documents.
What I got out of it can be summed up as follows.
If I read everything right the Eloi definitely qualifies under the mileage classification for a "Two Seater" which would only appear to require 31.6 MPG . (That's from the average MPG charts) Not clear from the standards whether that's combined or not, but I think the number I saw for Elio combined was about 60 MPG.
The issue that might be problematical is the "Car" thing. But it would probably never have gotten past the first stage if the DOE was going to play the definition game.
Chapter II of title 10 of the Code of Federal Regulations part 611.206 appears to give some priority to the Elio project since the factory is currently sitting idle and is over 20 years old.
With that said, I'm sure that Elio had professional help in making their request since government grants and loans are something you need a specialist, or team of specialists to do right.
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With regard to District 7 Caddo Parish Commissioner Stephanie Lynch.
Lynch was elected to the Shreveport City Council on Nov 4.
Why do I have a feeling that we haven't heard the last of her?
You would be correct that the "car' question was indeed an issue at one time as the ATVM loan program did exclude vehicles which did not meet the NHTSA definition as a car however this was corrected with the passage of another bill which opened the ATVM program to any vehicle which could meet the 'Ultra Efficient Vehicle' requirement of carrying twp people in an enclosed cabin at minimum of 75 MPG and/or electric equivalent.
http://green.autoblog.com/2009/10/30/president-signs-bill-expanding-atvm-program-to-three-wheelers/
I also read the existing idle plant as providing EM some priority in the program.
In meeting notes from a Caddo Parish Commission meeting from May 2014 EM tells the commission that they had completed the ATVM application and were having someone review it so they did in fact do this the smart way which is not too surprising as EM has generally been pretty good at finding the outside expertise needed to tackle the various parts of this project.
http://www.caddo.org/AgendaCenter/ViewFile/Minutes/05202014-241
Discounting now City Councilwoman Stephanie Lynch at this point would likely be a mistake. While the plant is not inside the city limits I have no doubt she will use her position to speak out against this project and/or actively hinder the project in any way she can.