Sorry Janne, I meant to respond to your post yesterday and didn't get back to it. But as Hiro has correctly pointed out:
It looks as though your drive's mount point is not /mnt/Toshiba so putting this into the config file will not point the drive.
Issuing df or mount at the terminal prompt should list all mounts. From there you can take note of the mount path of your Toshiba drive.
It will be in the format of /somewhere/Toshiba or even /somewhere/somewhereelse/Toshiba, that's assuming the drive is actually called Toshiba on your system.
But whatever the case, you should be able to identify the drive from df and with that information, edit the config file as before and correct the entry.
If you are unsure, just post the output here.
With respect to the use of NTFS, yes it would be better to have the drive formatted as ext4.
On my own system, I had a lot of movies on my NTFS formatted drive that I wanted to preserve, hence the reluctance to format.
I suspect you may be in a similar situation. I meant to fix this before now but have been procrastinating.
The general steps would be to A copy the directories and files to another drive on the system, format the drive as ext4, then copy the files back. Of course fixing everywhere that refers to paths on the drive.
or B (If you have no alternative drive), the general steps are:
1. Shrink the existing NTFS partition.
2. Create and format an additional ext4 partition on the drive.
3. Copy the folders/files from the NTFS partition to the ext4 partition.
4. Change the RecordedTV path in tvheadend point to the ext4 partition. Make sure any other paths are adjusted also (E.g. Kodi's path to Movies) and everything works as expected.
5. Delete the NTFS partition.
6. Grow the ext4 partition to the full capacity of the drive.
Of course not forgetting to edit the tvheadend config file to update the mount point.
The above assumes that you have enough remaining capacity on the drive. If you have 1Tb of files to copy, you need 1Tb free space.
I wouldn't blame you if you decide to procrastinate also though : )
Hope this helps. Let me know how you get on.