Yes, you can

Yes, you can 只用国务院的推荐信拿到H1签证. I got my H-1B approval in this May base on the recommmendation letter from DOS through 加快(2 days).

Also, you can 自己办加快, please see the instruction of form I-907 for the detaied infromation about the premium processing.

I got DOS's letter in this January, still haven't got any response from INS for final waiver approval. When did you get the letter from DOS?