I love this sort of catering challenge but this is a ridiculous list you're dealing with! Veggie / vegan with no gluten, tomatoes, pulses, lentils, onion, garlic, soy, spices or Quorn. And a low carb option?
If you're minded to do it at all here's what I would do
Breakfast - cereal or toast, gluten free toast available, the oat milk queen can bring her own and milk the individual oats if she's minded to. Jam, honey, marmalade and marmite on offer. If you were feeling generous, hardboiled eggs and cheese for the low carb crew.
Lunch - I'd avoid sandwiches and instead have a good selection of bread rolls, breadsticks, GF breads with lots of hummus, cheese, and fruit. Massive green salad (leaves, cucumber, peppers, celery, etc) and a massive quinoa salad (quinoa, finely chopped peppers and cucumber, chopped dried apricots, grated carrot, orange and cumin dressing). Various veggies like carrot sticks and radishes, pickled onions and gherkins.
Dinner - day 1 I would do jacket potatoes with toppings: vegan mushroom stroganoff, cheese (normal and vegan), hummus. If the low carbers are lifestyle preference rather than medical need, jacket sweet potatoes for them. If it's medical need, giant roast mushrooms - two each depending on size - instead. If you're doing the mushrooms, I'd do a veganised creamy leeks, or a spinach and chickpea mix, as a topping for the potatoes and mushrooms instead of the mushroom stroganoff, otherwise you're serving mushrooms with mushrooms.
Day 2 I would do rice bowls - prep all 18 bowls with half rice and half stir-fried green veg, a mixture of Chinese leaf, pak choi, shredded cabbage (no rice for the low carbers) and then have toppings available for them to help themselves: teriyaki jackfruit, sweetcorn, mushroom strips, maybe sweet and sour tofu knots (label for the soy allergic person), maybe broccoli and green pepper in black bean sauce, maybe sea spiced aubergine.
The teriyaki jackfruit would have to be made with aminos not soy sauce, and the onion / garlic averse person would have to stick to the sweetcorn and mushrooms (maybe the tofu knots) but that caters to everyone.
Snacks I would just do tea and biscuits. Oreos and bourbons are vegan. Dessert would be fruit and yoghurt. Vegan option would be coconut collaborative yoghurt not the soy one.
Then I would put my feet up with a large cup of tea and a bar of chocolate, and if one of them chooses to gaze sadly into a glass of water I would let them get on with it. It will be compensated by the person who was intolerant to the mere idea of food until they saw it. Both of these people are inevitable at any reasonably sized catering event.