“We’re shooting low-budget stuff (interviews and fun videos for web) so we’re not looking for anything like the 5D Mark II but still want something with good sensors and good compression quality.”
While availability is difficult, I’m guessing you will find the Panasonic GH2 an ideal choice. It’s feature set, including an auto-focus system that is quite impressive, and glass that is much cheaper yet still quite beautiful, will serve your stated needs well. The kit, with camera and 14-140 lens (with IS) and the 20mm 1.7 (IS) will set you back less than 2K as well.
An excellent review of cameras here: https://philipbloom.net/2010/12/07/whichdslr/