Hi - have you had any tests done (echo, ecg, stress test, etc.) to know if there is an underlying cause? I don't know anything about Hashimoto so maybe you are saying that is the underlying cause?
I have been in trigeminy before and agree it can be quite unsettling. I found sometimes that doing 100 jumping jacks would help mine break out of that rhythm, but I had done a number of tests and was told mine were "benign" so to speak.
Anyways, hope you are feeling better now!