I'll answer to just about anything, Allan...and I've been called a whole lot worse.
First. Origins of "sedan." I did a bit of digging and many sources state that the origin of the word is obscure when it comes to its use as a "sedan chair" or automobile body style. I'm gonna have to argue with Wikipedia a bit because they state, "a sedan is always closed." I guess no one told 'em about a convertible sedan...which is something of an oxymoron, but was used in the 30s and 40s pretty extensively. This seems to be the best explanation of its etymology:
"1635, 'covered chair on poles,' possibly from a southern Italian dialect derivative of It. sede 'chair' (cf. It. seggietta, 1598; the thing itself was said to have been introduced from Naples), from L. sedes, related to sedere 'sit' (see sedentary). Since Johnson's conjecture, often derived from the town of Sedan in France, where it was said to have been made or first used, but historical evidence for this is lacking. Introduced in England by Sir Sanders Duncombe in 1634 and first called a covered chair." I had plenty of experience with saloons, but let's just say that I don't do that anymore.
Coupe or Coupé DOES originate from the past tense of the French verb, "couper" (to cut) so, yeah, it's a "sedan" with the rear seating portion cut off:
"1825–35; < French coupé (in defs. 1 and 2 short for carrosse coupé cut (i.e., shortened) coach), past participle of couper to cut off"
Having given the term "Edwardian" some thought, it would be comprehensible to those in the UK, but much less so in the US and probably pretty close to meaningless to those in the far east and perhaps South American and Eastern Europe, although I'm sure members like Faksta understand it. Given that premise, I'd suggest that a more "global" term be used. I did more research and found that the VCC of the UK defines things exactly as you stated but in the same book where I found it states that the so-called "vintage era" begins in 1919; I take this to mean a return to motoring "normalcy" after WWI.
If the term "Brass Era" was used instead of Veteran and/or Edwardian, it could cover that time span, but it wouldn't really be accurate, since brass fittings began to be replaced with painted or plating of other types somewhere between 1914 and 1916...and I'm sure there are plenty of exceptions to that statement. So Brass Era wouldn't be my choice of verbiage.
Maybe the way to do it would be to use years only:
Pre-1919 which I don't like because it makes 1919 a questionable year, so I'd prefer 1885-1919, using the year of the first Benz car as the older boundary and 1919 to correspond with the end of WWI.
Pre-1920 might be a better term.
1920-1942 as a "between the wars" era.
1946-1975 I suggest 1975 because it was the "beginning of the end" for US muscle cars following the Arab oil embargo. I don't really know how this affected cars in Europe or other parts of the world, but it was a point of major changes in the US.
1976-present. This might be broken into two eras, 1976-1999 and 2000-present being "21st century" examples (I know...the century didn't actually start until 2001, but for the sake of round numbers.....)
If period names are discarded for the purpose of this "directory" then there's no ambiguity: either a car falls into a category or it doesn't. WWII presents a small problem, but I suppose the "between the wars" era could be extended to 1945, especially if no period names were used.
Quick note. In US square dancing, the term "Do-Si-Do" is derived from the Cajun patois and does indeed mean 2 by 2, same as the dos-a-dos, back-to-back seating arrangement, opposed to vis-a-vis, or face to face.
Again, comments, changes, opinions, suggestions are requested and welcomed.
RtR