Coarsely shred enough zucchini to make 2 1/2 cups. Toss in a colander with 3/4 tsp. salt and let drain. Very thinly slice remaining zucchini lengthwise, preferably with a handheld slicer, and set aside.
Heat 2 tbsp. oil in a large nonstick frying pan over medium-high heat. Add mushrooms, shallot, and garlic and cook, stirring often, until mixture begins to brown, 5 to 6 minutes. Reduce heat to medium. Stir in 1/2 tsp. each salt and pepper and the coriander and cumin. Cook until fragrant, about 30 seconds. Add flour and cook, stirring, until lightly toasted, 2 to 3 minutes. Remove from heat.
Whirl almonds in a food processor until finely chopped. Add rice, mushroom mixture, and eggs and pulse until rice is chopped. Transfer to a medium bowl.
Squeeze shredded zucchini a handful at a time to remove as much excess water as possible and add to rice mixture; stir until well combined. Divide into 4 portions.
Toss long zucchini strips in a bowl with 1/8 tsp. each salt and pepper and 1/2 tbsp. oil; set aside.
Return nonstick frying pan to medium heat and add remaining 2 tbsp. oil. Set 1 portion zucchini mixture at a time on a wide spatula and shape into a 3 1/2-in. patty; slide into pan. Fry patties, turning twice, until deep golden brown and an instant-read thermometer in center reaches 160°, about 15 minutes total. Squeeze a little lemon juice over patties.
Spread muffins with mayonnaise. Set patties on muffin bottoms and top with tomato, onion, and a loose pile of zucchini ribbons. Set muffin tops in place.