How do I pass the input of a step function startExecution to the executed function

I'm trying to use a step function startExecution state to break up a state machine into 2 parts and I want to pass the input of the startExecution function to the executed function, e.g.,

"Process chunk": {
            "Type": "Task",
            "Resource": "arn:aws:states:::states:startExecution",
            "Parameters": {
              "StateMachineArn": "arn:aws:states:us-west-1:12345:stateMachine:Ingestion-process-parts",
              "Input": "$.input.MessageDetails"  
            },
            "End": true,
            "ResultPath": "$.input.MessageDetails"
          }

where the startExecution input is

"input": {
    "MessageNumber": 0,
    "MessageDetails": "<an S3 URL>"
  },

but no matter what I try for the input to the executed state machine it just passes a literal value, i.e., in the case above, instead of passing the input of the startExecution state to the executed function it passes

"input": {
    "MessageDetails": "$.input.MessageDetails",
    "AWS_STEP_FUNCTIONS_STARTED_BY_EXECUTION_ID": "arn:aws:states:us-west-1:1234:execution:Ingestion-Chunk-CSV:055ede1a-dc03-4412-a341-d3b6611dbed4"
  },

Note that the same input parsing Does work for the Result:

{
  "name": "Process chunk",
  "output": {
    "MessageNumber": 0,
    "MessageDetails": "<an S3 URL>",

It doesn't appear the the normal approach of parsing the input using $... works for this purpose. Is it possible to do what I want?

thanks