Wow that's a lot to deal with!
Seems a lot to put a cat through surgery with all the associated risks while already waiting for I131. I know it's done now but did the vet even talk with you about other meds, or Hills y/d? Anyway, it's done now and you are where you are and can only go from here.
We went through the I131 last year in April. Molly's uncontrolled T4 was 70+ and controlled with the diet I didn't stick to religiously this immediately came down to 30. She is unpillable so we had no choice about management while waiting for treatment. Knowing that 70% of cats need a second operation plus then meds for life, and 30% have that extra material in the chest and end up at I131 anyway, for us it was a no-brainer. I do totally agree with your choice, it's the gold standard treatment - I'm just not sure I understand your vet insisting on the surgery first. My own vet has a HT cat that has had the second surgery and is HT for the third time.
There is a lot about radioiodine treatment on this forum, notably these two threads
viewtopic.php?f=13&t=6300&hilit=i131 and
viewtopic.php?f=13&t=5958&p=44314&hilit=i131#p44314 which make a lot of reading material but it's really helpful. My experience is pretty much all on the first one about Mouse do I won't repeat it here. Whilst it's an expense I will still be paying for until the end of next year and a trauma I would not care to repeat, it is absolutely definitely worthwhile and if any future cat of mine gets that diagnosis I would do it all again.
The vet hospital I used which is thankfully local to me is Langford, a world renowned centre owned by the University of Bristol (UK). My problem was Molly's psychological issues which they didn't fully appreciate. If your girl is ok with being handled and has stayed in a cattery before, it really is very simple and straightforward. Langford chose not to do scintigraphy but they did do a battery of tests that cost more than the treatment itself over 2 days, 4 weeks before the treatment, which included full chest and abdominal x-rays, scans, detailed bloods, uninalysis and more. The report I got back included blood pressure details, liver enzymes which were elevated more than they should have been for HT, as well as any bone changes and those all important eye and heart changes. Molly came back a much more chilled cat and thank goodness her appetite and weight are now much more normal.
They also didn't check for malignancy for two reasons. First, only 2-5% of thyroid tumours are cancerous. Second, it's quite simple, if it is cancer it won't respond to treatment and a very high dose with much longer in isolation will be needed to deal with it.
The other thing I don't understand is why you have to choose the dose and why it's 80 or 100 and nothing in between. Langford calculate the precise dose and order it individually for every patient. The assessment is done with the HT controlled, then the treatment is done uncontrolled so I had to take Molly off her diet and give her normal food for 2 weeks before treatment.
T4 is often still high or goes low post treatment but it takes time for the cat's system to settle. I don't know if the same applies with surgery but 4 months seems a short time between surgery and radioiodine if it does apply.