Okay first, we have some great basenji rescues in Texas thanks to BRAT and to Pam Hamilton with Camp Basenji.
I am quite dismayed about them not responding. That truly is not like them! If I were you, I'd contact them and just ask what is up. I will contact someone and alert to this thread. Hopefully you can find out what is up.
How old is your child now? It seems the older one is grown, but I think you indicated you had a 2 yr old child around 2007 or 2008? It could be the ones in your area are not good with kids. But looking at their page... they have very few listed... so it just simply may be that right now, not many available. However, ASK.
The other option is Camp Basenji. Since she has experienced homes with placements there, an adoption from her Florida rescue might be arranged.
http://www.campbasenji.org/