Becasue the H2/4 are so infrequent I think your best bet would be to:
1 – take a Capital Bikeshare bike from Petworth to Tenleytown (via Porter) and then hope on a 31,32 or 36
2- take a Capital Bikeshare bike from Petworth to Dupont and then hop on a D2
3- green/yellow to archives and hope on a 32/36
4 – buy a bike and enjoy the extra hour you get in your day.