It really is a horrible noise bar-biting. Not sure if this helps, but ours was never a bar biter until we went on holiday and left him somewhere else. When we came back he was doing it - and it was an attention thing to want to come out and also it was a bit of a stress thing I think due to the change of environment. I decided to ignore it eventually and he used to stop after we'd left the room. Now he's out of the habit again. If he's in your bedroom you can't go to bed and leave the room though!
The general thought is cage size and enough enrichment to keep them happy in the cage to help prevent it. Unfortunately though it can become a habit they just do after a while and if you have a bar chewing hamster that won't stop, a perspex or tank style cage would be better. I know you say you got him a bigger cage, but just wondering if it's big enough? If their cage is too small they will be stressed and want to chew their way out, especially at night when they are most active.
Miniimum recommended RSPCA size is about 80cm by 50cm continuous floor area - ie in one unit, not 2 or 3 smaller ones. They also need quite deep substrate/litter on the base of the cage so they can dig a bit, a house or hide that is big enough to build a nest inside, and chews to keep their teeth from growing to long. They also need out of cage time regularly as well, even if it's only 15 minutes every other day. Getting them into a routine of coming out around the same time can help so they know they will be coming out of the cage at some point.
Sorry if you know all this already.
It's horrible when you have spent money on a cage and then more money. I would agree with Penguine that a duna cage would be a good idea. The maxi duna multy costs over £60 though. You could make a bin cage (it's a large plastic box basically that you cut holes in and mesh them) but it's quite a bit of diy and a few tools required.
If you could get the money together I think the Maxi Duna Multy would solve the problems though. Your hammy would have lots of space and room for lots of enrichment, hides and deep substrate for digging tunnels, no bars to chew on (the top grid isn't an issue as they can't hold on to chew those bars) and that would solve the bar chewing and you could enjoy your hammy again. You could sell your current cage on ebay and that should get about £20 at least towards the new one.
It's a really nice 'cage' too because you can see them through the clear top.
Cage Maxi Duna Multy
It's quite big at 100cm long but would probably fit easily on top of a chest of drawers with a bit of overhang at the sides maybe, and it's a bit of a hamster heaven having the space.
Here are some pictures of set ups
https://www.google.co.uk/search?q=Ma...ed=0CAcQ_AUoAg
Does he have a wheel big enough as well? If his current cage and wheel are big enough then it probably is just a case of a solid sided cage, but if his cage and wheel are too small I'm not surprised he's bar chewing. I think if I had just one small room to live in and a chair that was too small to sit in and nothing much to do in there I'd be chewing to get out too!