フクロウ [梟]
No no, ええ is different from えい, you're not wrong about that and you definitely shouldn't change your pronounciation to make them sound the same all the time. Like I said, I really can't explain very well how it works (someone else up for it?), it just makes sense to write it as かれい... I guess ええ gives me more of a sense of two different sounds instead of just one long sound. Though sometimes えい can be pronounced like in the exclamation "えい!!!”, which is different from just a long え sound, sometimes it is very much like just a drawn out え, for example (scroll down to the Japanese pronounciation) http://www.forvo.com/word/%E6%88%90%E5%8A%9F/ has a sound in 成 that is basically the same as カレー's last sound, kind of. Like I said, I'm bad at explaining this, I've just been going on intuition most of the time. If you want to get a good pronunciation, the safest bet is probably doing what Magamo always recommends. That is, using Audacity or a similar program to record native speech, record yourself copying the thing while listening to the speech, comparing the two, rinse and repeat.