Here's the solution.
I fear I have to confess it's more a question of an XY-Problem. I mainly needed to get to Katwice, but I really wanted to re-visit Lwiw. In the last days of my journey I found a solution and would like to share it with you. You have to understand I needed to be in Katowice in the morning of the next day, so my time-budget was limited.
I decided to take an early bus from Kamjanez-Podilsky to Ternopol (as I recall it it was at 8am and I arrived at 10am - there are earlier ones too. The ticked I obtained straight at the station the day before). I had around 3h to see Ternopol (which is not that many, but I enjoyed).
Then I took the train from Ternopol to Lwiw and arrived at around 5pm.
From here I beg you: Please be smarter than me!
Don't do: Stay in Lwiw over night and take the early flight from Lwiw to Krakow, then the bus to Katowice. Lwiw got pretty expensive and even a cheap hotel was not so cheap as in other parts of Ukraine. I forgot to do the check-in at in the evening and had to pay a penalty at the airport of 55€. From Krakow I got a Flixbus to Katowice.
Also I sent my whole luggage from Kamjanez-Podilsky back home.
Total extra costs: Around 150 Euro.
Do: Stay in Lwiw from 5pm to 10pm and take the night train to Krakow. Then the morning train to Katowice.
I used to do something like that back in 2009, but was not very happy about it. In retrospective of the current trip it's still much better.