You're right that that cage is much too small for any hamster. He will be chewing the bars obsessively because he's bored - it's not a good trait as it can cause teeth damage and it's a sign of mental distress.
In terms of the cages, the ones that tend to be recommended are
Savic Hamster Heaven
Zooplus Alexander Cage
Zooplus Barney Cage
Zooplus Alaska Cage
So the only one from your list that is unsuitable is a Rotastak Homezone
In terms of toys and accessories that Syrians enjoy, this is a really good thread
Top 5 buys?
You also need a wheel that is big enough - if he has to bend his neck or back to run, then it's too small and will cause spinal problems. Most people recommend a 12" wheel, with the Karlie Wonderland, Trixie and Silent Runner being three of the most popular options.
In addition to the time in his ball, is he getting any handling time? That's a good time to let them explore. I like to play with my Syrian either on the bed or the sofa.