Thanks for the replies.
At this point I got a reply in the live chat of Coinomi mobile wallet (cool), I was told to send the BSV to my Coinomi BCH address, now I got same amount of BCH back.
I was told to start the split again with their tutorial and using the Coinomi wallet where my BCH is now.
Waiting for TX to confirm now, looks OK so far...
That was a bit stressful

It confuses me a bit that I need to start over in Coinomi BCH wallet and not my initial BCH core/abc wallet; because I consider this BCH in Coinomi to be "new" after the fork, but we'll see ...