Cook the crushed pineapple, brown sugar, dairy-free butter, and lemon juice over medium heat for 10 to 12 minutes, stirring regularly, until thick and glossy. Fold in the maraschino cherries, then refrigerate the swirl until cold.
Heat the oven to 350 degrees F and line a baking sheet with parchment paper. Mix the flour, cane sugar, baking powder, and sea salt, then stir in the dairy-free butter, oat milk, and vanilla until chunky crumbs form.
Bake the cake crumble for 11 to 13 minutes, stirring once, until golden. Cool completely, then freeze the crumble.
Whisk the coconut milk, oat milk, cane sugar, cornstarch, coconut oil, vanilla, and sea salt in a saucepan. Cook over medium heat until steaming and lightly thickened, then refrigerate for at least 4 hours.
Churn the cold vanilla base according to the ice cream maker's directions. Add two-thirds of the frozen cake crumble during the final 2 minutes.
Layer the ice cream with the pineapple cherry swirl and remaining cake crumble in a freezer-safe container. Freeze for 4 to 6 hours and soften briefly before serving.