The sequence you're describing proves the box is booting from eMMC. CE (and LE) are both dependent upon the vendor u-boot install which resides on and boots from eMMC storage. However, when you run recovery boot, either via the "reboot update" command or from using the reset button, vendor u-boot looks for u-boot script files, finds them, reads them, and this modifies the early boot environment to look for non-Android boot files. CE and LE use the same process to subvert Android and boot Linux, but configure u-boot to look for slightly different boot files. Hence after converting the box to CE and then triggering recovery mode (reboot update) with the LE card inserted it searches for and finds LE files and no longer finds CE files. To switch back to CE (either on SD or eMMC) you need to invoke recovery-boot mode again. This is normally done using the reset button: press the button (and keep it pressed) then power the box on and release the button at the right point (typically 6-7 seconds into boot) and u-boot searches for boot files again and will find CE scripts on a CE creted SD card. It's not a simple button press after power-on and LE has no ability to run "reboot update" commands that need Amlogic drivers that don't exist for newer Linux kernels. Now, it's unlikely but not impossible that your box vendor hacked Amlogic u-boot code to remove support for recovery boot and the button does not work. It's also possible that due to age or abuse the reset button has mecahnically failed. In that case you can still recover the device back to Android using the Windows based Amlogic flashing tool and a factory recovery image for the box, which are often found on vendor websites or forums like 4pda.
See what happens if you place LE boot files (on the LE SD card) with CE boot files (SYSTEM, kernel.img and the correct dtb.img). Rename kernel.img to KERNEL and configure uEnv.ini to look for a dtb file called dtb.img). Not guraranteed to work, but simple to try.