In my opinion, the best thing to do is to be honest and to explain that $A$ is the statement of main interest and that one is forced to prove the stronger statement $B$ just for technical reasons.
So I would call the statements Theorem $B$ and Corollary $A$ (since $A$ descends from $B$, after all), or maybe Theorem $B$ and Theorem $A$ if I intend to further emphasize the importance of $A$.
I think it is also convenient to write a remark explaining why the proof argument does not work for $A$; in this way, the reader will be motivated not to skip the proof of $B$.