I tried it once. And like you, it really wasn't effective. I seldomly got it on the field. And never hit anything good off it.
I think the problem is in the numbers. Because
Sunbird's Invocation is 6 mana, you have to be able to cast big mana spells. First you have to cast SI. Then you have to cast another big spell. Then, in order to really be effective, there has to be another big spell (but not too big) towards the top of your library. Because even if you're digging 8 cards deep, in a library with still 80 cards in it, that's still the top 10%
Sunbird's Invocation requires you to have many high CMC cards; and it also requires that you have the ability to hard cast those cards. If you can do that consistently, then you don't really need
Sunbird's Invocation. At least, that was my conclusion.