You are not just hypothyroid but severely hypothyroid. You must have been miserable when your temp was 94f.
Iodine is only part of the solution in raising body temperature.
Until you can find a lasting solution to the thyroid, which may involve more than one avenue, do the best you can every day to keep your body temp as high as possible. You can get a hang for this by measuring your temperature throughout the day and soon enough you will learn what behaviors/foods/etc work to raise it and which lower it.
Some A blood groups do well *leaning* toward a vegan diet, you don't have to be strict, but usually A's tend to shy away from heavy/fatty meaty diets because they can't process these things due to lower stomach acid and intestinal enzymes not designed for meat. It sounds like you are already doing this.
Supposedly soy isoflavones or in plain english soy can support type A thyroid function. Yes, everyone is always whining about how soy destroys thyroid function, but for A's it is certainly worth a try for you.
1300-1500 calories is WAAAAYYYYY under. I'm not sure if you are intentionally calorie limiting or you just feel so horrible when you eat more, but in any case you need to slowly start working your way toward at least 3-4000 calories per day or more. Well, wait a sec, if you are kapha dominant this might be too much, but more on that later.
Simply undereating can be a huge stress on the whole metabolism and could be considered a cause for hypothyroidism. No gas in the in tank, no energy.
I'm always skeptical of any type of set-in-stone diet like the fruit only, meat-only, etc, but just for now in your shoes I would try both the esselstein type diet which is high in starches and also the fruit calorie diet which is high in sweet fruits. See which, if either, you improve on.
Pittas will naturally gravitate toward sweets and do well on them. Kaphas might have a sweet tooth but it will not be good for them.
Both kapha and pitta would not do well on excess salt, so that seems to be the case, but there could be more going on. The experts usually recommend eating salt to taste. If you have salt cravings , but at the same time it causes edema then it's more complicated. If you feel better eating low salt then that's sort of easy.
Have a look into adrenal fatigue symptoms on cz or other sites and see if you fit. Thyroid problems are usually tied into adrenal problems, but one is usually primary. If you have a decent amount of energy, sleep well, good blood Sugar regulation, then adrenal fatige is probably not primary for you.
Now keep in mind when you take Iodine and co-supplements it is very important to increase calorie intake accordingly. You are essentially putting your foot on the gas pedal with Iodine and without fuel you will definitely make things worse.
For macro nutrients there is no need to make it complicated. All I meant was to generally have a sense of what proportions of protein/fat/carbohydrate you gravitate to. It should be very obvious to you if you give it 30 seconds of thought.
The common denominator between kapha and pitta is dry and astringent, so lots of astringent types of vegetables would probably be good for you.
You said your weight is constant no matter what you eat, well in that case you may as well eat what you like and enjoy while you are trying to figure this out. If your constitution is kapha dominant and you were this way since childhood then perhaps weight is not a good goal to chase. But, your thyroid is definitely out so that needs to be addressed.
I didn't see many carbohydrates in your diet, so here again could be a missing link. kapha pitta carbs would be apples, berries, dry grains, basmati, etc
Don't use sodium selenite form of selenium.
Supplements - only take them if they make you feel better.
kapha-pitta liver congestion is like a double whammy as both can contribute in different ways.
I would say for now make your priority body temperature. Everything ties in of course like diet, but you need to raise this and get it stable over 98.6 asap.
Try to find out if you are kapha dominant. Aversion to dairy and salt/edema are two big kapha flags.
Do you like spicy foods?
How are you in hot weather?
Are you prone toward lung problems, coughing, congestion?
Is this a longstanding problem or did it begin suddenly at some point?
How many Amalgam fillings do you have in your mouth?
Do you naturally drink a lot of water or have an aversion?
Test the brassica vegetables on yourself to see if they make your thyroid functions worse (lower your body temperature/metabolism)
Get a hair mineral test from ARL, TEI or Doctor's data.
Don't supplement potassium, get it from fruits and vegetables.
Also have to throw parasites in the mix too as a cause, but you have to sort through things one by one until you get a sense of what is primary.
Kaphas would usually be able to do a lot of exercise with relative ease, and at the same time not lose weight.
Did you body type change at a certain point in your life, ie you were rail thin up until a certain age.