You can fix that with a little tinkering in the NLA editor.
First you set up the animations in the Action editor like you normally would. Add the markers manually. Each action needs two markers called "youractionname:start" and "youractionname:end". It is important to not have the area defined by the markers overlap.
Once you are done with that, open the NLA editor and start adding the animation strips by pressing Shift+A. Now the next thing you have to do is to move around the action strips (the pink lines) to the corresponding marker area. If you see some bits overlap, you can always move the markers around in this mode too.
If you did everything correctly all the animation sequences should show up in the exporter.
I'd have never figured this one out without the help of Tophius.
Barnabas, if you could make a nice, detailed animation tutorial for BL, I would be very grateful. I know how to animate (actually do the key framing), I just can't get it set up for BL.