cdk-remote-stackでslashを含まないSSMパラメータを使おうとしてハマった

import * as cdk from 'aws-cdk-lib';
import { Construct } from 'constructs';
import { RemoteParameters } from 'cdk-remote-stack';

export class CdkStack extends cdk.Stack {
  constructor(scope: Construct, id: string, props?: cdk.StackProps) {
    super(scope, id, props);

    const parameterPath = '/some/parameter'
    const parameters = new RemoteParameters(this, 'RemoteParameters', {
      path: parameterPath,
      region: 'us-east-1',
    });

    const paramA = parameters.get(`${parameterPath}/aaa`);
    const paramB = parameters.get(`${parameterPath}/bbb`);

    new cdk.CfnOutput(this, 'ParameterAOutput', {
      value: paramA,
    });
  }
}

Received response status [FAILED] from custom resource. Message returned: Error: An error occurred (ValidationException) when calling the GetParametersByPath operation: The parameter doesn't meet the parameter name requirements. The parameter name must begin with a forward slash "/". It can't be prefixed with \"aws\" or \"ssm\" (case-insensitive). It must use only letters, numbers, or the following symbols: . (period), - (hyphen), _ (underscore). Special characters are not allowed. All sub-paths, if specified, must use the forward slash symbol "/". Valid example: /get/parameters2-/by1./path0_.