Hashimoto's thyroiditis is irreversible in the vast majority of cases with the exception of rare cases of remission. It is usually necessary to treat Hashimoto's thyroiditis for life and your thyroid replacement dosage may have to be adjusted from time to time.
The newest Korean study [Lee, M. et. Al. "Bone Mineral Density and Bone Turnover Markers in Patients on Long Term Suppressive Levothyroxine Therapy for Differentiated Thyroid Cancer," Abstracts of the American Thyroid Association Annual Meeting, 2011] found long term suppressive levothyroxine therapy does not affect bone density or increase the prevalence of osteoporosis.
I agree that you should not stop taking your pills; your TSH will go up again, and your FT4 will come down; you don't want that.
Your symptoms are typical of hypothyroidism, which is caused by the Hashimoto's.
You will most likely have to be on the thyroid replacement for life.