Cara, it's unlikely that you actually burned 300 calories in 20 minutes on the treadclimber. The calorie readouts on cardio machines are highly inaccurate, sorry to say. Manufacturers all try to out-do each other in the supposed calories that their machine burns so people will use it and buy it. But they're usually way, way off.
A better way to judge calories burned is by checking your heart rate, either with a heart rate monitor or on the machine. Your heart rate determines the number of calories you're burning. So if your heart rate is 150 (for example) on the treadclimber, 150 on the elliptical, and 150 on the treadmill, then you're burning the same number of calories on each piece of equipment, regardless of what the machine says.
My HR monitor tells me that I only burn about 60% of the calories that the Precor elliptical says. I believe the HR monitor, not the ridiculously overinflated Precor number. A LifeFitness crosstrainer tells me that I burn even more calories at the same heart rate, which is obviously wrong.
So ignore the machine readouts. If you don't want to invest in a HR monitor, use the Fitday activity that most closely matches what you did. I'd say that a stair climber is pretty close.