Okay I had to look at the old Shaw map to figure out if this was in Mount Vernon Square or Shaw or both. The answer is both. The Mount Vernon Square historical district overlaps with parts of Shaw.
The the other question was, “Is this the church on New Jersey Ave?” Yup, 3rd Street, New Jersey Ave, same diff apparently. That little section between Morgan and New York Avenue, has northbound traffic going on New Jersey and southbound traffic on 3rd Street.
The Third Church of God appears to continue on as the Third Street Church of God. In the 1957 survey their address is listed as 1204 3rd Street NW. Looking at their history listed on their website they wrote: Continue reading 1957 Church Survey: Third Church of God