Sorry for being such a pain…
Now running the script and found that it barfs at not finding the parted command…
Apparently either parted is not installed or it is not on path (neither for osmc or root).
A bit into the script it uses parted as follows:
SRC_BOOT_PARTITION_TYPE=`parted /dev/mmcblk0 -ms p | grep "^1" | cut -f 5 -d:`
SRC_ROOT_PARTITION_TYPE=`parted /dev/mmcblk0 -ms p | grep "^2" | cut -f 5 -d:`
I don’t know what other potentially non-existing commands it will use further into the process, is OSMC stripped down with regards to admin tools?
sudo apt-get install parted
We don’t include tools that most users will not use but they are al available in the repository
OK, thanks.
I will have to read through the rather big script to see what tools it actually does use then…
What it does is that it creates the partitions existing on the source on the target and then copies over the existing file trees. Thus it does not touch disk areas not holding files and the effect is that it will always succeed if the sum of the files is less than the available space. Win32DiskImager OTOH makes a bit-by-bit image of the SDCard and it turns out that same size cards are not really same size so it will fail to clone a disk if the target is smaller than the source even by a few non-used bytes…
Does OSMC come with a tool that can do this (making a disk clone only handling actual files) so I could use that instead?
EDIT:
And just to correct my statement that my mediadrive was not shared:
After I unplugged it and then re-inserted it into USB it did appear as a shared drive! 
Now I am at the exact same state as I was when I updated from my original OSMC 16.1…
All goes according to some plan until a Kodi screen is reached where it says (my translation from Swedish):
Kodi
v 17.0-Krypton
Add-on migration - please wait…
And it never continues, it just sits there for about 2 hours now. I.e. it is stuck there.
So this is on a brand new SDCard where I started with the image from Dec 24, 2016.
I then applied my latest Kodi settings backup via the MyOsmc program add-on and was back at the time before my earlier attempt to upgrade. This time a system, which had not been subject to any test of Kodi betas at all.
And still it does this…
So now remains to do what? As @fzinken suggests:
sudo systemctl stop mediacenter
sudo systemctl start mediacenter
Or something else? It did not work the last time…
And this time is no difference…
Tried it but all of my media has disappeared from the places where they were located earlier, like House Of Cards from TV-shows etc. There is no sign of any of the scraped content at all. 
If I navigate in file view I can reach the files themselves but instead of a descriptive episode title all I see is the non-descriptive file name.
How could this happen with a release upgrade?
Try removing the Addons database file.
It seems like one of your addons or skins is likely incompatible with the new release.
Kodi v17 images have been published on the website.
Yeah, I had seen that but I tried to upgrade in order not to have to figure out how to rebuild my libraries again. So I started with the 16.1 image and loaded back my kodi settings from the backup (this worked).
Then I tried the MyOsmc upgrade hoping it would carry over the libraries and general GUI.
But it did not work. I have now spent a few hours trying to figure out how to get the libraries on to the new upgraded Kodi17, but was only half successful.
It seems like in some categories the menu item to add a source to the library has disappeared…
There is only a “Update library” item and this seems to try to scan as best it knows everything I have on my disk.