Originally reported in https://github.com/localstack/localstack/issues/2099, the CreationTime for CF stacks was hardcoded. This was fixed in in LocalStack itself (https://github.com/localstack/localstack/pull/2103), but is now also fixed in moto (https://github.com/spulec/moto/pull/2818).

I don't know what version of moto you're using, and whether it's acceptable to use dev-releases, but if you do: 

moto 1.3.15.dev550 should fix this issue, so the LS fix can be removed if you upgrade :) 
'parameters': {
                'restApiId': 'RestApiId',
                'resourceId': 'ResourceId',
                'httpMethod': 'HttpMethod',
                'authorizationType': 'AuthorizationType',
                'requestParameters': 'RequestParameters'
            }
        }
    },
    'ApiGateway::Method::Integration': {
    },
    'ApiGateway::Deployment': {
        'create': {
            'function': 'create_deployment',
            'parameters': {
                'restApiId': 'RestApiId',
                'stageName': 'StageName',
                'stageDescription': 'StageDescription',
                'description': 'Description'
            }
        }
    },
    'ApiGateway::GatewayResponse': {
        'create': {
            'function': 'put_gateway_response',
            'parameters': {
                'restApiId': 'RestApiId',
                'responseType': 'ResponseType',
                'statusCode': 'StatusCode',
                'responseParameters': 'ResponseParameters',