NSF Proposals: numerical citations or author-year?
In terms of reference formatting, this is the only paragraph I can find in the NSF guide:


  Reference information is required. Each reference must include the
  names of all authors (in the same sequence in which they appear in the
  publication), the article and journal title, book title, volume
  number, page numbers, and year of publication.


Thanks to @Suresh, I misunderstood the meaning of it and I agree that the instruction does not specify either numeric or author-year format.

However, the page limit is 15, all inclusive, numeric system would give you a few more lines at the end. And you don't need to hate flipping back and forth, because the reviewers will do the flipping. However, should you feel so strong against it, call and talk to the grant program manager or contact person and ask if you can use your preferred system.