From the perspective of cloning a running system the issue would be if the filesystem changes during the clone. Many services can run which only alter RAM, and remounting the filesystem read-only is the best way to be certain it isn’t going to change.
The concept of adding extra storage to the PC is actually a very good way of dealing with this. A thumb drive on the PC, or an SD card on the PC, or an external USB SATA drive would all be good choices for a clone destination. “dd” can be used in combination with ssh to directly stream the dd output to the PC’s external storage media. Or you could plug a second USB media directly into the Jetson. Clone methods can simply be chosen which do not cross partition boundaries or filesystem boundaries and you’d get the correct content (using recursive cp would fail).
You can clone from one SD card to another directly on the Jetson, but again I must emphasize that it is best to have the rootfs mounted read-only during the process. This is nothing unique regardless of hardware or version of Linux, this is a general “should always do this if cloning”. If you suggest which destination you want, then more specific instructions can be added. Normally you will find the difference between methods to be how the filesystem is set to read-only during the clone.