For the crab cakes: In a large bowl, combine the crabmeat, rice, mayonnaise, scallions, Dijon, tarragon, seafood seasoning, egg and lemon zest and juice. Stir to combine. Season with salt and pepper. Sprinkle with 1/4 cup of the breadcrumbs and stir them in. You should be able to make a crab cake that just holds together but is still a bit wet. If the mixture is too wet to hold together (and it might be, depending on how wet the crab and cooked rice are), stir in up to 1/4 cup more breadcrumbs.
Using a small ice-cream scoop or tablespoon measure, scoop out the mixture by heaping tablespoons, then form each into a small cake and place the cakes on a sheet stray. Refrigerate for 1 hour to firm them up.
Heat the canola oil and butter in a large nonstick skillet and preheat the oven to 200 degrees F. Spread about 1 cup breadcrumbs on a plate and lightly dredge the crab cakes in the breadcrumbs. Working in two batches, fry the crab cakes until golden on both sides and heated through, 2 to 3 minutes per side. Drain the first batch on paper towels and keep them warm in the oven while you cook the second batch. Season the crab cakes with salt.
For the aioli: Combine the mayonnaise, tarragon, basil, dill, lemon zest and juice. Season with salt.
For serving: Serve the crab cakes alongside the aioli or place a dollop of aioli on each. Serve with lemon wedges.