In case it helps others, I ended up following the advice from this answer on another forum post.
Essentially, use the app.config.js
functionality to add the (as far as I can tell totally undocumented?) AndroidConfig.Permissions.withBlockedPermissions
plugin to remove the permission.
import { AndroidConfig } from "@expo/config-plugins";
export default ({ config }) => ({
...config,
plugins: [
[
AndroidConfig.Permissions.withBlockedPermissions,
["android.permission.WRITE_EXTERNAL_STORAGE"],
],
],
});