When I first got Luna she chewed her bars, I had to work really hard at it to try and work out how to get her to stop. I had just moved her into an Alaska Cage at the time, she is now in the Savic Plaza. She stopped for over a year then suddenly started up again, but she has stopped again now.
I found that things like these may help
https://smile.amazon.co.uk/Naturals-...ateway&sr=8-30.
https://smile.amazon.co.uk/gp/produc...?ie=UTF8&psc=1
Instead of chewing the bars, she would chew on these.
and i make walnut hanger things (idea from erins animals) so you can put food in the empty half shells of the walnuts.
https://www.youtube.com/watch?v=4POW...2&index=2&t=1s
any boredom breakers that distract them for a little bit - i tried to place things in the area that she was chewing.
Also I noticed she was chewing when she wanted to be let out, so I tried not to let her out then and would only get her out when she had stopped chewing and gone off to do something else. So she didn't associate chewing with being let out of her cage.
I hope you manage to help your hammy to stop chewing. I totally get how it's not nice to see, and if you aren't allowed a bigger cage, keep trying lots of different little things and hopefully something will help .