I should be long asleep (midnight over here
) but shortly want to get back at you already.
First of all my advice would be postphone RAI, please read around on the board (you can use the search function - posts from Sammy64 to name just one would be very useful). as you'll read RAI has many side-effects such as permanently hypoT but also increased risk for TED (thyroid eye disease).
Next to that a doctor who does not know how to dose properly before RAI wont know it either after (it becomes even more difficult afterwards due the rise in antibodies and their effect on TSH and most doctors being blindsided with TSH).
That being said, if you're properly managed on medication I don't understand why you'd need RAI. how are your antibodies these days? where those even tested?
standard is: start antithyroid drugs (such as methimazole); decrease the dosage once levels fall within normal ranges, dosing shoudl be done based on FT4 and not TSH and then maintaining dosage should be the lowest dosage possible keeping FT4 in the upperquarter of the ranges.
I know this is no longer of any use for you, the reason I mention this is, because 1) it might give you an idea whether you were dosed like that (which I doubt) since 2) if properly dosed the remission rate is very high (in order for that to happen it's important to keep FT4 high enough and avoid hypoT (i FT4 drops too low one becomes hypoT and that triggers antibody production). for remission to happen antibodies need to be low/decrease or gone.
At this point you're not hyperT (highly doubt it) so it's not a matter of remaining hyperT . a person has Graves and that can cause hyperT (too much thyroid hormone in the body) once properly treated, a person still has graves but is no longer hyperT. once in remission or when levels are at a good place, a person still has graves but no longer hyperT, in case of remission although one still has graves, treatment is no longer required.
hang in there and hope this helps some.