I think he'll stop bar chewing if you give him a wheel! As Luna says. They definitely need a wheel or they get loads of pent up energy. It won't make any difference to taming if he has a wheel - might make it easier actually. At night they can run up to 10 miles in the wild and that's when they do most of their wheel running. We had a syrian in a barney cage - much bigger - and the only time he bar chewed was when he didn't have a wheel. They also love their wheels - makes them happy!
This is a good basic wheel that fits the cage and suitable size for a syrian
https://www.amazon.co.uk/Trixie-6101...3558485&sr=8-1