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But there's a phone number you can call where you will get a random rep, and they're damn good. They even answer the phone, almost instantly.
There's an option when you call to "speak to a specific Googler" and you can use that option even if you don't have a "dedicated rep". So, if somebody is working on a problem for you, or some rep has been particularly helpful, you can ask to talk to them.
I won't post the phone number or where to find it online (you CAN find it online) because I've given up trying to work around the TOS here to give out useful information.
So, I'm afraid I'm left with giving tantalizing but useless teases or talking about the weather...
As I understand it, they have different accounts for adwords' big spenders. You may have the wrong type of account (an online account). Emailing someone at Google may rectify this.
Apart from that, what would I need a rep for? All my issues so far were solvable with the on-board tools and reports.