i know someone who has salicylate issues as well, maybe not quite as bad as you but there is a lot of crossover between the Blood Type Diet and foods he can eat. so you should look into that if you know your blood type.
i think moritz is a good way to go if you can handle it. it will be a leap of faith, and better to do a strong flush rather than a weak one.
if you are taking in a fair amount of sodium in your diet and are able to drink enough fluid then some saunas could help you out a lot, getting rid of metals floating around, cleaning up some damage. but you have to be drinking and absorbing what you drink, especially sodium. fir saunas are really good, but cost a bit of money and you'd have to get out of the house to try it. if you are in oz, you could sit in your car on a really hot day with the windows closed to simulate a fir sauna.
some of the juices you mentioned like zuchini will pull out heavy metals and make things worse temporarily.
i didn't mention the primal diet to you yet because i didn't want to overload you with information, but that is something that would likely work for you. it costs money for quality food, and takes a lot of dedication, but you could dig yourself out of a hole in a few months or more.
rice and ghee is a good combo because the liver will react strongly to plain fat, and protein also can activate your pancreas and gall bladder. but fat and carbs together slows down the absorption of fat and will not strongly trigger your gall bladder, so it makes sense to me, no mystery there.
a lot of people on the primal diet have dairy issues, but do ok with the raw dairy.
you could try something like raw egg yolk mixed with a bit of raw honey as a test, or add in some raw butter. don't put it in the same category as pasteurized dairy. most of the people who are in dire straits and start the primal diet have a similar situation with their livers not working at all.
you might do well also with just doing the cutler mineral protocol, but not chelating. he has a list somewhere on internetland with the basic minerals that all the mercury people should be taking, calcium, magnesium, zinc, selenium, molybdenum, c, b complex, etc in specific dosages 4x a day. that list isn't complete, but the real list contains the bare minimum for keeping mercury from damaging you. you should also look into sulfur foods and see if they aggravate you, i'm guessing yes.
give the salt baths a try too just in case those tests you took aren't the whole story.
i think regular peroxide is ok in baths, not sure, maybe check on another forum to be sure. drinking it is a different story though.
i wouldn't get your fillings out yet, your health is too precarious. wait until you stabilize a bit and then consider it. i doubt you will find anyone to do surgery in your home, nice thought though.
check into lemonade specifically as a drink as it can help a lot with energy... fresh lemons only, raw honey and a pinch of salt.
i think in ayurveda your situation would be an extreme vata imbalance which would indicate salty, sweet, or oily foods, everything well cooked, small portions, sunlight, no bitters or strong spices. something like mayonaise might work with some carbs. you can google vata imbalance and find 10,000 sites.
since you actually are able to tolerate fat with carbs, there are likely other combinations that will work for you if you keep digging. you can also try cooking or stewing your fruits in a bit of fat or ghee to help ground yourself. pears are not indicated for vata disorders.
i'm not sure if chanca piedra is a high salicylate food, but it is very good at relaxing the biliary system, so that's worth a try too. moritz uses that herb a lot with people. actually moritz's whole spiel is basically ayurvedic diet plus Liver Flushes plus some mumbo jumbo magic stones and chanting.
the proteins recommended for vata are white meats or white meat seafoods, cooked in some oil or butter.
you may also get some mileage from oil massage. you can absorb a fair amount of oil through the skin and this could possibly start to nourish you a bit. sesame or coconut oil are recommended.
i'd' bet that down the road you find mercury to be a much bigger issue than the salicylates, even though now you are reactive to everything.
castor oil packs might be good for the liver but i think it's a high salicylate food. not sure if doing it externally would aggravate your sensitivity.