I (36F) also have hashimoto’s and have lost about 5lb in 6 weeks without much effort, just 18:6 and eating reasonably. Honestly if it’s under control and you’re taking your meds it shouldn’t be too much of a barrier. You should let your Endo know when you’ve lost some weight because they might want to do a blood draw to check your levels. Good luck!
I have Hashimoto’s and do IF. I’m not strict about the time frame, but generally anywhere from 16:8 to 18:6. I also count calories five days out of every seven so I know I’m not overeating in my window. If I’m eating relatively low carb, the fasting period is effortless. It’s great that your low carb/high protein diet will also cut out wheat and sugar as it’s not a bad idea to do this anyway with Hashimoto’s. Be sure to get enough protein with your exercise program and good luck.