That's the first thing I thought as well. And you wouldn't have to use much....Also wonder if using some SG in there would work better too?
I have a small ultrasonic cleaner that I use to clean jewelry and my glasses. Holds a little over 2 cups of liquid. For that I use a small capful of the cleaner they suggested. I'm guessing here... but your cleaner looks to be about twice the size... maybe 3 times. I think you could get away with less than a capful of Simple Green because it's so concentrated.
Then again... if SG is expensive to buy where you are (or worse if you have to pay shipping... I know how costly that is) perhaps something like a degreaser would work?
And yes... definitely run hot, hot water through your rig first....