yud is not vowel ee, yud is consonant like j, it changes vowel next to it. i don't know how correctly write these vowels on english, but they changed this way: a -> ya, e (like in lemon) -> je or ye, i -> yi. For example name אלנה will prononce Alena or Elena and ילנה is Yelena, not Eelena. So, it need to remember what vowel from these three was next to yud, because two other go with vav.
I don't want to start an argument because I don't live in Israel and it's your language to pronounce as you wish. But when I visit Israel as a tourist, and if I eventually make aliyah, I will stubbornly continue to pronounce the vav ha chibur as oo when it precedes בומף
I think your pronouncing the ו correctly in this case might be like an English speaker saying “asked him” with the k clearly audible; most people in conversation change the k to a t, at least they do in the U.S. so it ends up sounding like astim. If you don’t believe me, show the sentence “I asked him but he wouldn’t answer me”
to the person next to you and ask her to read it at normal speed.