I am an idiot. This is totally possible, but I had my service provider order wrong.

This is what I do now:

class AppServiceProvider extends ServiceProvider {

	/**
	 * Register services.
	 */
	public function register() {
		$this->app->singleton(MyFormBuilder::class, function ($app) {
			return new MyFormBuilder($app, $app[FormHelper::class], $app['events']);
		});

		$this->app->alias(MyFormBuilder::class, 'laravel-form-builder');
		$this->app->alias(MyFormBuilder::class, 'Kris\LaravelFormBuilder\FormBuilder');
	}

}

And that makes every call resolve to my FormBuilder. Injections, app() calls, everything. Perfect.