I went through the E-2 process a few years ago. IIRC you can pay an extra $1000 to make your application a "high priority" one, which cuts the guaranteed response time from something like 3 months to 30 days.
When I did it as a high-priority application, I got an initial response saying "we need more data" within 2-3 weeks (from what I remember), then the final approval 2-3 weeks after I submitted that info.
When I did it as a high-priority application, I got an initial response saying "we need more data" within 2-3 weeks (from what I remember), then the final approval 2-3 weeks after I submitted that info.