Yes, it IS an option to go there personally.
However, they don't accept the passports before at least a week after the documents have been received here in DC. My OCI documents were received in DC on the 9th of April, but when I went there on the 10th, they asked me to come back after a week. So I went there again this morning and submitted my passports. They said I can collect them all back tomorrow evening. So one more day and I will hopefully be done with the immigration departments in two countries, for a while at least!