"Doing it right" means doing it in a way that allows you to reach your goals while still staying healthy and sane.

If that means not counting vegetables, there are others who do the same and make it work for them. I don't count the green stuff I put in wraps and on sandwiches either because I find that I'm encouraged to add more of it when I don't count. (And believe me, that extra 20 calories a day from piling on baby spinach leaves is NOT what made me fat. ) As long as you count the stuff that goes with the veggies--the higher-calorie items like salad dressings, cheese shavings, and so forth--you'll still be in the right neighborhood.

Sadly, there's no such thing as a food that takes as much energy to eat and digest as it returns to you in calories. Even so, the caloric load of things like celery sticks is so low that you're probably pretty safe eating bunches.

"All or nothing" was my motto at one time too. I cannot tell you how freeing it is to realize that I am in complete control of this process--that I have the capacity to make my plan into something I can live with instead of something that feels like punishment, that it's totally okay to lose a pound and a half a week and enjoy the process instead of losing three pounds a week and being abjectly miserable.

About your hypothyroidism--are you taking replacement levothyroxin for it? The fatigue is wretched if your dosage isn't right, so if you're dealing with that, no wonder you're having trouble dealing with extra stress!

If you're trying to shave calories off, I'd also omit nuts and perhaps look at a veggie packed egg white omelet for breakfast. I add a piece of turkey bacon for 35 calories and a half of a bagel thin for 55 calories and I have a filling breakfast.
One of my favorite snacks is grape tomatoes or baby carrots with hummus.

I think that even if you go over your calorie goal, you will continue to lose weight.
I use the basic rule of 300 calories for 3 meals and 100-150 for 3 snacks per day= 1200 (min) calories per day. Of course, if you're going for more calories per day, you can add them to your meals as needed.
I love nuts, but when you're calorie counting, they're a killer! Most sample menu scenarios suggest about 10 nuts per snack- which isn't very much!
Overall, I think you're doing just fine!

This! Your plan absolutely must be sustainable for life to succeed.

I too have hypothyroidism and have been on replacement medication for 13+ years. Be aware that it make take much longer to start to lose weight than others that do not have this obstacle. I didn't start to lose much weight until I was at it for about 3 months. But when my body started to lose I lost 6-8 lbs a month consistently. YMMV. Just keep at it! Your body will have no choice but to comply.

Regarding your all of nothing thinking--throw that out the window. You goof up and overeat? Listen to your hunger. Maybe your next snack or meal doesn't really need to be that big of a meal/snack. Get back on track the very next time you eat, whether it's a snack or meal. Continual progress--that's what we are after here.