Proper ways to contact US academics from outside academia?
I am developing an application I believe would be a wonderful (free)
  asset to the study and comprehension of a particular subject for
  students and docents alike.


Consider presenting it at an academic conference. In my field, there are usually industry booths at the conferences. But there is also often the opportunity to present innovative software with a poster, or sometimes even as a talk.

Don't expect any responses to unsolicited emails marketing your software. These will usually be regarded as spam.