I can sympathise- I have an underactive thyroid too and LT was the ONLY thing that shifted the weight. If your results come back normal, I'd ask him to do some more in-depth blood tests to see if anything is 'red-flagged'. Something might show up?
A few other ideas...
I know it sounds mad- but you may be eating too little? The re-feed is meant to get you back to 'normal' eating asap so your metabolism doesn't suffer. If you're 'surviving' on two shakes and one meal- you're still in 'diet' mode and your body may be hanging onto every nutrient you put into it.
It could also be fluid retention? Salads & veg are mainly water-based, and if you're not drinking enough you'll hang onto all you take in?
Make sure you get protein with your meals- lean fish/chicken or eggs. Your body will start losing muscle if you don't (as you're eating so little) and it'll be a catch-22 situation as if you start to gain a little- you'll end up with more fat than before as you'll now have less muscle- if that makes sense? Muscle burns more calories than fat, so it's to your advantage not to lose any?
Failing all that- ask to be referred to a dietitian/nutritionist to see if they can shed any light on it? I was referred to one and they were pretty useless in my case, I was told I was eating the 'right' foods, in the 'right' amounts, cooked the 'right' ways, exercising 4-5 times a week, and they couldn't understand why I wasn't losing- but I wasn't! In desperation I turned to LT, and it worked. I'm maintaining a while now, and plan to return to tfr next week to hopefully lose the last stone or so.