My 17 year old cat has been hyperthyroid for 8 years. She's been on the liquid meds all that time, with no side effects. She's not on a special diet, either, although I do buy high quality food (Weruva, Felidae, etc.). For many years, all I had to do was get her T4 levels checked twice a year and she stayed pretty steady. We've been having more trouble for the last couple of years, so it's been more expensive ($60 a pop for the blood work), but we always manage to get her levels right after some fiddling around with the dosage.
I know vet care can be expensive, but the meds themselves aren't too bad. Good luck!
I want to free myself from the burden of inaction. I want to raise myself to any plane I can imagine. ---Crowded House