Be very careful! I had a General Practitioner give the same advice in 2003. He didn't believe in thyroidectomies and that my thyroid would “just eventually burn itself out.” He was very convincing. . . convincing enough that I ignored the Endo's advice to have a thyroidectomy.
Long-story-short, years of perplexing physical problems, eventual TED, sky high antibodies, tachycardia, near thyroid storm, etc.
Is your GP basing the dosage advice on your thyroid hormone levels or just general principle? Did your Endo explain to you (and did you understand) the reason for the dosage adjustment? Did it make sense after they showed you the test results and explained? Have you been tested for the Grave's and Hashimoto's antibodies? (I'd insist on this one)
Also, you can go in and out of remission after Methimazole treatments, or even after no treatment. Very frustrating, I know.
The best advice I can give is what you appear to be doing. Do your homework. Write it all down, print out articles, and take written questions to the doctor appointments. Have hardcopies of your test results so doctors can't tap-dance around and confuse things.
I'm not a doctor. I'm just a fellow thyroid compadre.
Hope all goes well in your treatments.
Lid Retraction TED 03/2010.
On the road to full health 04/2011.