I'm willing to bet you don't hate queueing on the phone more than I do.
Any trick for advancing you to the head of the queue doesn't do anything to encourage the company to improve their Customer service - it just means someone else has to wait longer. My method makes MORE work for the company so they do at least have an incentive to improve.
I can't pretend I always do this but I've done it a number of times. If you don't get someone owning your problem within, say, 10 minutes, hangup and write them a letter. Include all the information they need to fix the problem. Stress that you had to resort to mail because they would not deal with your problem on the phone. Give them your phone number. Tell them you will be cancelling your direct debit on x date if they do not contact you. Obviously you don't have a DD to the bank but whatever financial penalty you can impose on them - maybe move your account elsewhere. This usually prompts some action. Send the letter recorded.
When they finally deal with your complaint they may threaten to come after you for their losses (if any) but they won't - they'll lose if they try because you have it in writing that you had to resort to writing a letter due to their appalling service.
Indeed, I often state in my complaint letter(s) that I will be charging them for my time at some rate per hour for every hour I have to help them solve their problem.
I don't think you have this in the US but in the UK we have a concept called Small Claims Court (EDIT: just seen on another SE site that the US DOES have a small claims system). An individual can lodge a claim against ANYONE for a financial loss. I have used it a couple of times and I've threatened companies with it too. They will definitely bend over backwards to solve your problem rather than get involved in a court case, it costs you virtually nothing so there's no real loss if it all goes wrong for you.
If the company don't solve the problem within a reasonable time, file a claim against them for your losses and your time.
Another answerer here has suggested that poor service is the price we have to pay for cheap services. Wrong. The organisation has chosen to pitch their services cheaper than the competition to gain business. If they can't afford to provide the service they have taken on, they should do their sums properly just like we have to when we decide if we can afford to buy a new car or new house. In the meantime, they should bite the bullet and provide the service they have voluntarily entered into a contract to supply - even if it means making a loss to do so.