Citation style for research statement
No sane search committee member is likely to care about your citation style as long as it looks "professional." Nobody is grading you here, so really, you're just looking to avoid raising red flags.  

So, what is "professional"? By that, I mean that it looks pretty much like something that they would likely see in a publication.  Most fields have a range of citation styles found in different publications, and thus pretty much anything that fits within such a range is likely to not be remarkable, and your goal for your citations is simply that.

One last note, though: it seems that your choice of citation style is being dictated significantly by inertia of familiarity with APA.  Since you will likely be required by future publications to use a range of citation styles, you may wish to switch from manual citation to using citation management software, which will help simplify compliance with a wide range of styles.