@.access:
I don't remember Law saying he wanted to personally kill Doflamingo, I just remember him saying his plan was for Kaido to do it and the reason he originally lied about going after Kaido was just to trick Luffy into an alliance (probably taking a Shichibukai down wouldn't look as interesting as an Emperor).
I don't see an inconsistency there, but I agree Law doesn't really have any personal reason to be on the alliance at this point to take down Kaido as he never cared about Kaido at all. I suppose he is only there because the alliance he made with Luffy was meant to go there, so even if he didn't intend to at first now he is stuck to it as long as Luffy is still willing to go. Seems like a weak reason to risk the life of his whole crew (just to honor an accord), but I suppose they are all in agreement with this.
As for no hint of Law/Doflamingo connection in Sabaody, probably Oda hadn't come up with that. He said the supernova didn't even exist in his notebooks until right before their introduction, so, yeah…
Well Bepo his first mate is from Zou. And they are part of of the alliance to take down Kaido, so Law is at least indirectly commited to the operation.
And don't forget that Law didn't plan to come out alive from Dressrosa. He was willing to sacrafice himself just to make Kaido kill Doflamingo.
So actually he owns his life to Luffy and now stands to his word as Luffy stood to his.