Well the route depends are you sticking to asphalt or are you keen to do some unpaved roads (which are in really decent condition).
Now as Croatia is part of Schengen I highly recommend that you go with paved path by the Danube from Mohacs to Draž. Literally no traffic at all and you are cycling besides the Danube, and it takes you to Batina. Better than your current plan via Udvar imho.
Now if you are keen to do some unpaved roads, Serbian side is way more interesting, you would cycle all the way from border to the Bogojevo/Erdut (with exception to going through Apatin). Distance in this case would be same as you would go through Croatia.
This is the way I would go.
If you aim the asphalt, then on Serbian side you would have +15km to Vukovar but still better than through Croatia.
I am talking about entering to Serbia at Batina border.
And if I cross the border at Nestin rather than by crossing over to Bačka Palanka, how do I then switch back to the left bank in order to get to Novi Sad?
Two ways, first one is to take the ferry from Beočin to Futog and then from Futog you have the bicycle path to Novi Sad. Or the second way is to cycle to Sremska Kamenica or Petrovaradin and from there you cross the bridge directly into the Novi Sad.
And what do you say about the part of the route after Novi Sad - I heard people saying it's rather bad, and better avoided by getting on this new fast train?
I don't have any first hand experience, but I also heard people hate to cycle it. This new trains are cheap, just a few euros and pretty fast.