Have you tried to handle it as an error and retry?

  Retry": [ {
    "ErrorEquals": ["S3resourceNotFound"],
    "IntervalSeconds": 1,
    "MaxAttempts": 2,
    "BackoffRate": 2.0
  },

  "ErrorEquals": ["OtherErrorName"],
    "IntervalSeconds": 1,
    "MaxAttempts": 2,
    "BackoffRate": 2.0
  }]

Simpler.

I couldn't figure out how to return a named error from a python2.7 Lambda function; as far as I could tell it would always return UnhandledError. How'd you do it?

I don't think you can set custom error names from a Lambda function:

"Important Custom Error Names, like those shown above ("ErrorA", "ErrorB", etc.) can be generated by an Activity, but not Lambda Functions. (See "FunctionError" field in the Lambda Response Syntax for more information"[0]

[0] https://docs.aws.amazon.com/step-functions/latest/dg/concept...

Yeah, I was wrong.

Just read the AWS Step Functions Developer Guide (1.0) and it's not currently possible to generate custom named errors from a Task. Only possible from Activities.