Maybe I'm missing something, but we know exactly what Bernard would have said first from statement 2.
He says, "At first I didn't know", so all he could have said if he had spoken first would have been "I don't know when the birthday is". Then Albert would have said, "I don't know when the birthday is, and I knew that Bernard couldn't have".
So the problem is unchanged regardless of who speaks first.
It also doesn't seem that cryptic to me... It doesn't take that much reading between the lines to understand the statement "at first I didn't know, but I know now" to mean "the information that Albert just provided gives me enough information to determine the birthday"...
That doesn't make any sense to me. Can you post exactly the sequence of statements if Bernard speaks first?
Simply reordering the questions does not make sense, so I can't see it happening any way other than what I posted, which shows that it wouldn't change anything.
That breaks the whole problem because you've removed the part where Albert says something that gives Bernard the information he needs to work out the date.
I don't think it's really a good critique of a logic problem to say, "but if you remove this extremely important part, it doesn't work anymore"!
The conversation would need to be:
Bernard: I don't know when Cheryl's birthday is
Albert: I don't know when Cheryl's birthday is, and I knew that Bernard didn't know.
Bernard: Then I know when Cheryl's birthday is now.
Albert: Then I also know when Cheryl's birthday is.
Then it works. You only have to assume that the parties are logical and tell the truth.
He says, "At first I didn't know", so all he could have said if he had spoken first would have been "I don't know when the birthday is". Then Albert would have said, "I don't know when the birthday is, and I knew that Bernard couldn't have".
So the problem is unchanged regardless of who speaks first.
It also doesn't seem that cryptic to me... It doesn't take that much reading between the lines to understand the statement "at first I didn't know, but I know now" to mean "the information that Albert just provided gives me enough information to determine the birthday"...