I think I have it figured out.
To get the filesystem image, I did:
dd if=/dev/mmcblk2 | ssh -C myuser@mycomputer 'cat > disk.img'
Then, I downloaded the U-boot "firmware recovery image" from Compulab. I'm not sure this is correctly named. I decompressed the zip file, and it has two flash files inside the zip file. I'm not 100% sure, but it looks like you choose the flash file based on the amount of memory on your Compulab. I used flash.bin.d2d4.
Then, to flash the system, I plugged into the programming port and restarted the device. Then I ran:
uuu -b emmc_all flash.bin.d2d4 disk.img
This resulted in a fully working system.