AWS policy actions for querying a CloudWatch log group and extracting information from the results

I am trying to query the AWS CloudWatch logs that are created by a Lambda Function. I have written a script to do this, which does the following:

1. aws logs start-query
   Submit a query, with the appropriate time window and query string.

2. aws logs get-query-results
   Return the log record pointer results from the query created in step (1).

3. aws logs get-log-record
   Dereference the log record pointers from step (2) to get the log stream IDs.

4. aws logs get-log-events
   Fetch the log events from the log streams found in step (3).

This works and now I'm trying to create a policy that will allow me to run all of the above without authentication. This is what I've come up with, going by the AWS CloudWatch Logs permissions reference:

{
  "Effect": "Allow",
  "Action": [
    "logs:DescribeLogStreams",
    "logs:GetLogEvents",
    "logs:StartQuery",
    "logs:DescribeQueries",
    "logs:GetQueryResults",
    "logs:GetLogRecord"
  ],
  "Resource": [
    "arn:aws:logs:REGION:ACCOUNT:log-group:/aws/lambda/FUNCTION",
    "arn:aws:logs:REGION:ACCOUNT:log-group:/aws/lambda/FUNCTION:log-stream:*"
  ]
}

Unfortunately, this causes my script to fail at the second step. I can successfully create a query, but when I try to fetch its results, I get:

An error occurred (AccessDeniedException) when calling the GetQueryResults operation: User with accountId: ACCOUNT is not authorized to perform GetQueryResults

What am I missing? Clearly GetQueryResults is allowed, but it's still not working. What other actions do I need to allow for both step 2 and what follows to succeed?

It turns out that GetQueryResults and GetLogRecords should not be limited to a particular CloudWatch resource and instead applied to everything. The following fixed the problem:

[
  {
    "Effect": "Allow",
    "Action": [
      "logs:DescribeLogStreams",
      "logs:GetLogEvents",
      "logs:StartQuery"
    ],
    "Resource": [
      "arn:aws:logs:REGION:ACCOUNT:log-group:/aws/lambda/FUNCTION",
      "arn:aws:logs:REGION:ACCOUNT:log-group:/aws/lambda/FUNCTION:log-stream:*"
    ]
  },
  {
    "Effect": "Allow",
    "Action": [
      "logs:GetQueryResults",
      "logs:GetLogRecord"
    ],
    "Resource": "*"
  }
]