It sounds like you're shooting RAW here. The 1Ds Mk III buffer should be enough for 12 RAW images; is your camera becoming unresponsive after the first 5-7 frames or is it after the buffer is full? Given the size of the images coming from your cameras, I would expect the speed at which you can shoot, once your buffer is full, to drop to about 1 or 2 fps (the 1Ds Mk III writes up to 45 MB/s). It sounds like you're pushing the maximum write-performance of the camera. There are a few solutions, but they're probably not that palatable for your work:
* Slow your shooting rate,
* Get a camera with a larger buffer (the D3X apparently has a RAW buffer large enough for 20+ images),
* Lower the capture quality (Not sure what the Canon side of things can do, but, for example, reducing resolution, compression, file format, or image aspect ratio, or number of bits in A/D conversion)