The 1861 Regulations don't mention the corps because it wasn't officially established till August 2, 1862, in AOP Special Order 147, which specifies the green half-chevrons mentioned in the initial post, as well as green hat bands. The Order doesn't say you can only wear a sack coat or you have to remove other distinctions, so it seems reasonable that the green half chevrons and hat band would be in addition to whatever other piping you had on your uniform.
But this only applies to the Army of the Potomac. The act of Congress that extended the Letterman system to the entire army came out on March 11, 1864, and states that the uniform or distinctions will be whatever "the Secretary of War shall deem proper." I haven't found a subsequent directive on this, though there may very well be one. But I would think that as long as Letterman was Medical Director of the AOP, from August 1862 to December 1863, there would have been some adherence to his instructions for the corps in that army.
M. A. Schaffner
Midstream Regressive Complainer