A TSI of 80 will effect your thyroid function.. but it isn't high enough to classify you as Graves. I have TSI levels over 120.. in addition to TPOAb levels in the 1000's.

But then my immune system always does things in a big way. I get Graves and Hashimoto's symptoms.
Now it has been documented that Graves patients or Hashimoto's patients with their compromised immune systems often develop the opposing thyroid AI condition as a means of self-defense. It is odd but in some their system seems to recognize that destroying the thyroid tissue is resulting in a decrease in thyroid hormone function. The system also realizes that the TSH trigger of TPO and TG T4 production and transport mechanism is causing said destruction to occur at a higher rate. Developing the Graves trait TSI (thyroid stimulating immuglobulins) is a back door method around the TSH.
I concur that given your presence of autoimmune antibodies for both Graves and Hashimoto's that you should check the secondary TRAb graves marker. Your swing from hypoT to normal may just be a result of Hashitoxicosis. The fancy name for a Graves-Hashimoto's terf war over you thyroid. In the end people with Hashimoto's and Graves antibodies end up with a dead thyroid and classified as just being Hashimoto's... or at least that is what four Endos have told me. I had two Endos that ignored my Graves all together because my Hashimoto's was som dominant over the Graves. However I do have mild thyroid eye disease... which the non-Graves acknowledgers just say is the result of a rare Hashimoto's interaction. *snort* Whatever. I am not using an Endon't at the moment. I actually like forward progress in my thyroid, adrenal, PCOS, IR, and reactive hypoglycemia treatment.
MG
ANY presence of thyroid antibodies be they Graves of Hashimoto's is abnormal immune function. However clinical positive Hashimoto's and Graves standards are based on statistical averaging of known antibody levels in patients with Hashi's or Graves that show positive symptoms. So you have to look at the presence of antibodies in addition to symptoms. If the symptoms are there and antibodies are present.. it is PROBABLE that said patient has Hashimoto's or Graves. Diagnosis is not black or white.. there is a LOT of grey in it.
Hashimoto's antibody tests are TPOAb and TGAb ranges vary between laboratories
Graves antibody markers TSI and TRAb ranges vary between labs as well. With Graves however studies show that remission in over 90% of active Graves patients doesn't occur until the TSI levels fall below 25 on a positive scale of 125. Many will have an immediate re-emergence of symptoms if antibody levels are between 100-125 and ATDs are withdrawn.