I don't buy for a moment that the unit needs $425 in cleaning. He's simply adding on to boost his profit on a job that won't get him much in the way of money from the warranty company. In essence, he's using you to pad his profit, so I'd say screw him.
This sounds like a gas unit.
Gas units aren't exactly known for their dirty combustion, or difficulty keeping them clean.
"Unless that thing is very new chances are you just can't replace the heat exchanger."
Every gas furnace I've ever seen, the oldest going back to one manufactured in the 1930s, with most made in the 1960s to 1980s, have had heat exchangers that can be relatively easily removed and, if necessary, replaced.