Here's where the power of Android comes into play. Sorry it's so late of a reply by the way. Was just looking through the Android forum.
Unfortunately I've never seen this as an option in any camera apps I've used. However, this, along with a lot of other things people THINK you can't do, can be done easily with Tasker.
Set up a scheduled task to run however often, I'll let you determine your trigger yourself. I tried to find a clever trigger like when closing the camera app or something, but I didn't come up with anything at a quick glance.
Now, as for the action, just tell it to run a shell command, and write out an "mv" command for your phone. For my phone it would be something like "mv /storage/sdcard0/DCIM/100MEDIA/*.mp4 /storage/sdcard0/DCIM/Movies/".
The only problem with Tasker is that it's a bit raw. For example, I'm not sure what would happen if it tried to move a movie that was being actively written. I suspect the file system would lock the file and not allow it to move, in that case it should just pick it up next time around. One other thing that maybe someone can help me with, I don't know if mv is a command you can access without root and busybox, or if mv is accessible from Android already. I'd think it is already included, and since you're moving files on your sd card, you wouldn't need to worry about root access to access the files. If you do have root access though, all the better and I just wrote up the action really quick on my phone and verified it worked.
So, maybe not the solution you wanted to hear, plus Tasker costs money (but is entirely worth it if you ask me), and I don't want to guarantee it would work perfect, but I just come up with solutions to problems and that's the first one I thought of for this situation.
Oh yeah, I knew there was a way to do what I wanted. You can make the task run as an exit task on the camera application. The only thing you'd have to consider then is how long the camera app might sit in the background before it's actually killed, but at least that should stop you from having to use a schedule and stop you from having to worry about the file being grabbed while being written still.