First-make sure that this thoracic disc herniation is causing your long-tract signs (“hyperreflexic lower extremities, weakness/heaviness in both lower legs and sensory changes”). The cervical spine is more commonly involved in cord compression. An MRI of the cervical spine would rule this condition out.
If the thoracic disk herniation is causing the cord compression and myelopathy, then you do have some choices. Kyphosis of this level should be over at least four and hopefully five to six segments to make a posterior correction viable. If the spine is not kyphotic over at least four segments, the correction probably would not allow the cord to drift far enough posteriorly to decompress it.
Percutaneous endoscopic discectomy is a good procedure performed by a well experienced surgeon. It is technically demanding procedure (this is one I do not perform) but has the least amount of dissection necessary.
The “direct lateral” is also known as the transpedicular approach and also can be successful.