I would use the camera's controls normally, not remote control, the only difference being it writes to the phone's storage over USB.
Short answer: You can't, at least not without writing custom software that runs on the phone. The only way for these cameras to save directly over USB without touching the internal SD card is using the CHDK
PTP extension, which requires a custom client. One could theoretically write a client for Android, but AFAIK no one has, and depending how Android manages access to PTP devices, it might require root.
Would it be possible to do this instantaneously after taking a photo, or would I need a seperate script to kick in at all? I remember having to switch SD card partitions in order to access photos on a computer, maybe a script would have to run to do that.
Partition swapping won't be an issue if your are using PTP to access the camera, the files seen over PTP would be the same as what the Canon firmware sees, which would be the large partition in a correctly configured mult-partition card.
As described above, you can't have shots saved *directly* to the phone at all.
You could theoretically write a script that allowed you to shoot while the cable was connected, and then subsequently make the camera visible to the phone to transfer photos using whatever method it normally does with PTP. This could be done by masking the USB bit using the USB remote setting, or possibly switching to rec with switch_mode_usb. This would essentially just save you connecting/disconnecting the cable, which probably isn't what you want, but I can provide more details if it is.