Methimazole is an excellent medication for Grave's disease and other forms of hyperthyroidism which works by interfering with the production of the thyroid hormones. It is generally well tolerated and has few side effects, but it does require close monitoring because of a low rate of some severe side effects, such as low blood counts. Typically, therefore, people on methimazole have to have periodic blood work to check for these side effects.
I would talk to your endocrinologist
about the management of your Grave's disease. Usually methimazole therapy is continued for a few years to see if remission of the Grave's disease can be induced. I do think it is a bit unusual to be on methimazole long term for 6 years as you have been. Since there is a relatively high rate of relapses of methimazole (as you say, you have not been able to taper off completely) and because of the long term potential for methimazole side effects, it might be time to discuss radioiodine ablation therapy of the thyroid gland, which is a more definitive treatment option for hyperthyroidism.
Your endocrinologist will be able to discuss with you the risks and benefits of these treatment options.