There is no need for an ultrasonic cleaner. You will get better results with vinegar or some acid. You dont have to remove the cap. If you get some phosphoric acid and pour it in the tank, fasten the cap and put the tank upside down for say a half hour, then check the cap and you should be good to go. Hell it might even be 15 minutes.
I think the ultrasonic cleaner is more of a fascination to you than anything else. I did the same thing with Soda blasting. The idea of it was super cool to me. Since you do not have one I suggest going a different route.