Hi,
I think it's...
eyed do..and you are right, there's only one D sound, but it's still different from
"eye do". This happens very often when there's a word that ends with a sound similar to the first of the following word. So, when you have two similar sounds, you don't pronounce both of them completely, but you join them together. In the case of
"eyed do", you should "hold" the first D (put the tongue where it goes for a D sound, but don't release the sound), and release the sound (= you actually do it completely) when you pronounce the second D. ---->
eye(d)-doIf you make both sounds, it'll sound like
"eye duh do", and that's not what you hear from natives <--- but Italians do that, LOL
Note that
"eye(d)-do" is not the same as
"eye do". It is true that you don't hear two D's in the former, but there's a kind of "pause" or "stop" due to the unreleased D that makes it different from the latter.
That's the way I see it