The hospital opened July 1898 and was closed by middle of October 1898.
Your Justus Goslau/Goslan enlisted in the Army May 18, 1898 at age 19 in Baltimore, MD as a Physician's Druggist, assigned Hosp Corps. He was discharged Oct 16, 1898 in Chickamauga Park, Georgia with the rank of Private, also noted was he was "excellent".
Doctors or Physicians held an Officers Rank in the U.S. Military, and Justus was only age 19, held the rate of Private and was listed in Army paperwork as a "Physician's Druggist", which does not a mean a Druggist that was a Physician. So it can't be "true" he was a "doctor" at Leiter Hospital.