[souffle]

I'm really not sure why she is smelling so bad but it does sound like a skin infection however you would expect it to present as showing some oozing a suppuration on the skin surface. A fungal infection may also show this way and can smell bad. It might cost a bit but would it be worth doing a skin scrape / swab culture to see if there was an infection?Mite treatment may help if she has come down with mite overgrowth and secondary infection.
Check out her housing. Is she sleeping in any enclosed hut / house or tube. These can cause bacteria to grow in the moist surroundings and make them smell awful especially if they are peeing in he house too. I'd suggest a large open nest made from piles of ripped up plain tissue or a large cardboard box with doors cut in it.
Bottle chewing may be the issue. Too much water can cause the whole body chemistry to change and the smell of the hamster will change too. The kidneys struggle tryingto get rid of the extra fluid and the liver can fail with the strain if it washing out essentials. Take the bottle out now and give a small heavy bowl. feed a good dry mix and veggies three times a week. Don't give the bottle back till you have seen if this helps.
Lastly there is the more serious issue of something like Cushings, a cancer inside or out or a major organ failure.
Try the simple things first then see if the vets can see her again. I hope she can be helped.