The trick, I have found, is to treat the other person on the line, as well, a real person. When they say their name, say it back to them, ask them how their day is, chat for a second about how it's their Wednesday (halfway there!), what the weather like where they are (Broncos are going to have a tough game, eh?), etc. Even just 30 seconds of chatter will get you great service. So many people treat them as 'the help', so when you come in and treat them as an equal human, their day just got a little better, and they'll treat you better too, because you treated them well first.
And I mean you really get better service. That direct line to their manager's manager? You have that now, just because you were nice. That bouquet of flowers for your mom/wife? It just got a little larger, because you asked them how their day is going. That bill you are having trouble paying? It's 15% off, because you complained about the snow too. Yeah, it's not a lot. Yeah, it happens maybe 1/10 times. But it is worth 30 seconds.
Besides, you got to make an actual human's day better. No one is too busy for that, for good manners and a smile, even if it's over the phone.