There is speculation that increasing cold weather was what may have been responsible for the Anasazi move from Mesa Verde to sites in other canyons.

(A) that increasing cold weather was what may have been
(B) whether increasing cold weather was what was
(C) that increasingly cold weather was what had been
(D) whether increasingly cold weather may have been what was
(E) that increasingly cold weather may have been

Do we 'speculate whether' or do we 'speculate that'?

Please explain