The recommended setup is to have one SkeletonAnimation per direction. Hide and show the relevant ones as needed.
SkeletonAnimation is not designed for rapid, subsequent switching of SkeletonDataAssets.
Every time you switch to using different SkeletonData, it needs to reinitialize. SkeletonAnimation reinitialization involves orphaning old data structures and creating new ones. This can be bad for both memory and performance; it will generate garbage and allocate and initialize new objects every time you switch.