The box is booting and working again 
Most of the credit goes to @0xbadbee without whose tireless help the box would certainly not be running…
Thank you so much for the great support.
For documentation purposes, I would like to write down what
has happened and how we were able to determine it and bring these box back to life:
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The file system of my Tonibox was screwed up…
Unfortunately, it was not possible to reconstruct how this happened -
I created a FlashDump from my box and searched it with binwalk…
binwalk was able to save my certificates from the FlashDump with automatic extraction.
Of course you can also simply read them from the dump in a HexEditor…
But using binwalk was way more convenient. -
At the same time, @0xbadbee “just” wrote a patch for the cc3200tool and uploaded it to the dev branch, which can extract files based on their file ID with some sort of tolerance against bad file tables…
Thanks to the patch we were able to recover many more files from my image. -
I was able to retrive the initial setup AccessPoint SSID from my cell phone, which I used for the first setup of the cloud connection. I was then able to enter the name in /sys/ap.cfg using a HEX editor, for which @0xbadbee sent me a template-file.
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The rest was piecing together several system images that @0xbadbee provided, the saved files from my file system, the service packs downloaded manually from TI (exact version ota_1.0.1.13-2.11.0.1.ucf, only with exactly this one ( neither later nor earlier version) my box was able to establish a WLAN connection again / communicate with the cloud server…
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Then , in this order, format the flash memory install the service pack, copy the file system over, reboot
cc3200tool -p /dev/ttyUSB0 --reset rts format_flash -s 4M write_file --signature ./spti/ota_1.0.1.13-2.11.0.1.ucf.signed.bin ./spti/ota_1.0.1.13-2.11.0.1.ucf /sys/servicepack.ucf write_all_files ./new_fs_2/
Thanks to all the other guys trying to help me out.