Hi lobsterfan
Welcome to NeuroTalk.
My understanding is that Hashimoto's Encephalopathy usually responds to oral steroids though the optimal dose of these is not known (it might differ between different people).
This might help you in discussing this with your neurologist
Hashimoto's encephalitis | Genetic and Rare Diseases Information Center (GARD) – an NCATS Program.
All the best.