Applied for an job with an incomplete description- should I contact the hiring manager with more information?

I applied for a job last week. I found the position listed on a semi-private forum, and I tailored it to match. Now, though, I just found the same job listed on Idealist. While it's clearly the same job, with the same title, this job description is more detailed and the contact person is different.

Because I didn't see the listing that was just posted widely, I didn't know that there was a large emphasis on field trips and college admissions in the job. I am very experienced with these topics, and I'm concerned that my original resume and cover letter won't be reflecting my full strengths.

Is it reasonable to send them a second email? For instance, I could write, "I forwarded my resume and cover letter to _____ last week, but I just found a somewhat different description for this position on Idealist. I am writing to emphasize that I also have a strong background in college admissions and would be eager to guide students through the admissions process." (Or something like that).

Is this reasonable, or will it just look like I'm applying for the same job twice? Should I just stick with my original submission and wait?

Thanks!