Sometimes you just have to take whatever job is there. For instance, I get up at 5:30 every morning to be in work by 6:30, I work in the sun, rain, wind, whatever and I have to carry some very heavy items which put a lot of strain on my joints.
I would absolutely love to have a job where I could go into a nice warm office environment and not have to worry about lugging wardrobes up flights of steps etc but unfortunately there are not that many jobs of that sort near to where I live and in any case, competition for jobs like those is harsh.
I would agree with you that Job centre staff can be a waste of time, so this is where you have to use your own initiative, this may sound harsh but don't forget that I have been an employer too. I would not think much of a person that a job centre has sent to me. I'd think that theat person wanted to have an interview so that he or she could carry on claiming benefit.
On the other hand, if somebody used their own initiative and wrote me a letter or came to see me in person and was dressed smart, was polite then I'd be much more enthusiastic about them.
I really think that if you wrote to 50 different government organisation human resource departments explaining your disability and that you were looking for a job, it wouldn't matter what the job was, you'd just like to work there and could you come in for a chat, then you'll get a job.
These places *have* to employ a certain percentage of disabled and ethnic minority people so in fact you have an advantage over someone like me in as much as you'd certainly get more interviews. I've tried to get jobs in government and it can be quite difficult. I couldn't even get a job as a grave digger ffs!
It comes down to whether you really want to work and if you really want a job then you'll be prepared to take any opening and do whatever it took to get one. Your hearing disability won't stop you. If you write to 50 government orgs explaining your situation and you don't get an employment offer of some sort from it then I'll personally pay your postage myself! Just write to the employers directly and stop relying on the employment service, you're wasting your time.