Have you looked at the Mi2 program http://www.gomi2.org . That’s the internship program designed by Southeast in partnership with LIA. That’s the best offering from Southeast. I’m not aware of other opportunities with LIA for anything greater than 2 weeks.
I don’t know much about Tenwek other than discussions with Dr. Stevens and Dr. White. I would suggest looking through the website and contacting them directly if you are interested http://www.tenwek.org/
Hope that’s of some help…
Soli Deo Gloria!