Has House of the Dragon changed the way Dany got her Eggs? 

I honestly didn't like that change at all, because it doesn't make sense. All those things you said plus the fact that Dreamfyre looks exactly like Daenerys' dragons and Syrax is nowhere near that, knowing that she's from a different breed. It's like a tiger giving birth to puppies. Just doesn't make any sense to me.

I agree. I understand why people conflate with the books and the show, but given how certain things are laid out, they are not the same.

I mean, if they just said that Dreamfyre’s old eggs were incubating at Dragonstone it all could have been avoided.

It is kinda fun if we get some changes from the book as it surprises us a bit, gives us all something to think about. As long as the changes aren't to big and stray to far from George's idea of it all.