resume - Explaining that experience is far greater than official job title implies

Hopefully this meets the FAQ under the 'Non-fiction, technical' section.

I work as a Graphic Designer, but I want to apply for a job as an Advertising Account Manager. While my title at my current job says "Graphic Designer," in practice I do a lot more then that. Our company is frankly pretty bad, and as a result our Acct Mgrs just try to lie and swindle to get clients to sign a contract; then they pass the file off to me to do everything else. They don't follow-up with me, they don't proof the ads, they don't do anything but convince the person to sign the contract - I do everything beyond that. On multiple occasions clients thought I was the Account Manager, because they end up talking more to me then with the actual Acct Mgr. I've also been responsible for some up-selling and finding new leads.

I do freelance on the side which means I am my own Acct Mgr for those clients. Part of being an Acct Mgr is being a good Brand Ambassador, and I've got experience in that area too - I served in the US Peace Corps, which is very much being a Brand Ambassador 24/7 in the "glass fishbowl," as they like to say.

Part of me wants to just explain the above without being negative towards my current job. The other part of me wants to write in a way that shows I understand the point. Something like

I am a creative, friendly, detail-oriented problem solver. I thoroughly enjoy analyzing questions and designs to make sure that they serve their point and are completely free of errors. For the work I do, that is to communicate an idea and create interest in a product or company. In the case of this letter it is to create interest in myself. If offered a position I would bring this same dedication, salesmanship, creativity, and outstanding attention to detail in creating an interest in both AGENCY NAME, and in our clients.

But I'm concerned in the above that it doesn't really explain my experience and my resume doesn't particularly show Acct Manager experience just Graphic Design experience. How could I better convey the above and also explain my current experience without it becoming too long?

The description:

AGENCY has an opening for an experienced and ambitious Account Director. This person will drive new business and manage creative marketing programs utilizing our full range of services—design, digital, strategy, and product development.

The Account Director will be responsible for developing a deep understanding of client needs and objectives, and managing resources to deliver relevant, integrated solutions. A successful candidate will be able to lead several multi-disciplinary projects simultaneously, while still identifying and developing the next great client opportunity. Expert communication, project management experience, and creative thinking required.

Job Functions: Account Management, Business Development & Sales, Design Management, Marketing, Project Management, Research, Strategy & Planning