Maybe I can help (if u'll consider using a Cheat)....
There's a "default" EDE ---it looks kinda worn, patched, n' beat-up. U get it in Primm, early in game.
The 2nd Ede ("advanced armor" model) is sleek, brighter & new-looking.
Ditto, the 3rd one (a sleek "advanced weapon" Ede).
The 1st Ede(the un-modified one from Primm) I'm always able to open his "dialogue wheel", but never
been able to open that wheel on the other the other 2 Ede's.
The Game "glitch' u mentioned, is probably the culprit.
I have a "cheat terminal" in my Pip Boy, that allows me to call up 1, or 2, or all 3 Ede's simultaneously.
I can fire any one of them, or fire all 3 at once---and re-hire them at any time.
I can make them 'essential' or 'not essential'.
I got it at www.nexus.com in the "Vegas Mods" download section. See link below.
When Cheat is installed, it appears as a terminal, right next to the terminal in Doc's house in Goodsprings.
It has an "option" that lets u use it on your Pip Boy (so u can always use it without returning to Doc's house).
The thing is awesome and has really freed and expanded my gameplay.
IMO, it might be the most useful Cheat in the Game---cuz it has other, powerful, features.
Until they patch the game (to get rid of that Wheel 'glitch') you might wanna consider using it.
30,000 Vegas gamers have already downloaded it.
When u open link below, go to page 3 or 4. Its called "Cheat Terminal".
http://www.newvegasnexus.com/downloads/cat.php?id=58&orderby=name&order=ASC