I will be arriving at Huaihua train station approximately a week before Chinese New Years.

As I know, there is no bus from HH to Chengdu or Chongqing. But train service is available to both cities. You may consider taking train.
But I'm afraid you need to book the train tickets in advance as the tickets are really hard to come by before the Chinese New Year. I personally suggest you contact TravelChinaGuide to let them help you with the train tickets booking. Their email is bookingtravelchinaguide.com. May help!