I reinstalled using the OSMC_TGT_appletv_20160130-HDD.img image and it worked as expected with prompt to remove stick and reboot.
Now OSMC is installed on internal HD and no frown face at reboot.
Just one issue:
After install I went directly to the app store to install SMB but I got an error.
I tried also transmission and cron but always get an error.
Logs: http://paste.osmc.io/qaqozuloru
Did you enable debugging? I can not see any try logs from the App Store.
Also maybe check only after a minute or so as it looks that your wifi connection is not connected when Kodi is ready started.