The information you provided decides the issue for Carter's 1st Tennessee Cavalry. On 1864 this command served with Vaughn's Cavalry Brigade in the Shenandoah Valley of Virginia. Members even crossed the Potomac River into Maryland as part of General Early's command, some coming within sight of the unfinished capitol dome at Washington DC at one point.

Sorry not to address your question, but I'd be proud to have an ancestor who was part of this campaign!