I've not used the EAI's, but I did use similar levers -- looking at the photo in your link, I wouldn't be surprised is those I used were beefier and stiffer -- back in the early '90s when some biggish name made these for use with bar ends; I used them with Scott AT4 or related mtb bars with the "bar ends" part of the bar.
From the straight part of the bar you'd 3-or-4-finger brake with your 3d, 4th, and 5th fingers pulling the straight part of the levers, but when you were holding the forward extensions you'd use your 4th, and 5th fingers to pull on the right-angled extensions. This worked, but only for speed modulation; you wouldn't lock the wheels from this position. I mean, they'd slow you down well, but not for panic stops.
Still and all, they were helpful, though, since I didn't use them long, they probably were not so very helpful that the simplicity and lighter weight of regular 2-finger levers weren't overall a better choice.
As for Moustache bars, I can't see the EAI levers being a great help, at least if your M-bars are like the very many I've used. IME and IMO, the best levers for M-bars are non-aero road bar levers installed somewhere along the forward-most arc of the bar, to be reachable from most riding positions.
I can't speak to Choco bars, since I've not used them.