It would probably be useful to know what went wrong, it shouldn’t be possible to brick or alter a JTX1 simply by copy of directory content to an external drive.
In terms of recovery the recovery mode simply makes the JTK1 a USB device which the flash software understands. Flash software can clone or read partitions, and although this is rather slow, you could clone a loopback mountable copy of the root partition.
Flash can install a system from scratch, or it can re-use an existing image (such as from your clone). Creating a new image takes much longer than re-using an existing image.
The cloned image can be loopback mounted and explored or edited, including fstab.
For information on cloned raw images versus compressed sparse images, and general details, see the K1 article (actual clone command differs, but other details are useful):
For clone commands on a JTX1, see:
Regarding rescue systems…
Basically if your “/boot/extlinux/extlinux.conf” file already had an alternate entry for booting to a different root partition, then you could use serial console and boot to a rescue or complete working system. You may find that your system still has some functionality if you use the serial console access, as this does not require any video or network driver. If this is the case you could add a rescue entry to extlinux.conf which points at an SD card or SATA root file system, or even edit fstab. The serial console setting is speed 115200, 8N1. For serial console, see: