CDK IoT createJob not working for documentParameters and AWS managed templates

Hi, This CLI command to create a job from an AWS managed template works:

$ aws iot create-job --targets 'arn:aws:iot:region:account:thing/thingname' --job-id 'test-aws-job' --job-template-arn 'arn:aws:iot:region::jobtemplate/AWS-Run-Command:1.0' --document-parameters '{"command": "ls","runAsUser": "root"}'

but this seemingly equivalent CDK custom resource doesn't. CDK deploy returns Message returned: Document parameters are only supported for managed job templates.:

const testAwsJobUuid = 'test-aws-job' + uuidv4();
const testDocumentParameters = new Map<string, string>([
  ["command", "ls"],
  ["runAsUser", "root"]
]);

const testAwsJob = new cr.AwsCustomResource(this, 'test-aws-job', {
  onCreate: {
    service: 'Iot',
    action: 'createJob',
    parameters: {
      targets: [`arn:aws:iot:${process.env.CDK_DEFAULT_REGION}:${process.env.CDK_DEFAULT_ACCOUNT}:thing/thingname`],
      jobTemplateArn: `arn:aws:iot:${process.env.CDK_DEFAULT_REGION}:${process.env.CDK_DEFAULT_ACCOUNT}:jobtemplate/AWS-Run-Command:1.0`,
      documentParameters: testDocumentParameters,
      jobId: `${testAwsJobUuid}`
    },
    physicalResourceId: cr.PhysicalResourceId.of(Date.now().toString()),
  },
  policy: cr.AwsCustomResourcePolicy.fromSdkCalls({
    resources: cr.AwsCustomResourcePolicy.ANY_RESOURCE,
  }),
});

Many thanks, Gary