Yi Alpha Strike randomness, plus how to beat turtles?

Lost a match the other day playing as yi jungle. I was super ahead, but entire rest of team was way behind. I split push our way all the way into their base, and even got inhibs a couple times. But the enemy team did well at turtling and staying grouped in base. We had no chance whatsoever of winning a teamfight by engaging on them, they had both Illaoi and Amumu.

Which brings me to my first point.... Why are the abilities you can dodge with Alpha Strike so freakin random. Found out that game that you can't dodge Illaoi ult with alpha? Tried several times and it never worked, wasn't sure if it was timing or lag, but it never did.

I know there are other random abilities than can and can't be dodged. You can dodge Ziggs ult but not Illaois? You can dodge Ahri charms and xerath stuns, etc... but you cant dodge bard stun? You can even dodge TF gold card with good timing. But it doesn't seem like there is any rhyme or reason to what you can and cannot dodge with alpha...

But also, what are some good strats to break a turtle like that when you know your team absolutely cant win a teamfight?