Trusted Advisor dashboard permission issue with management account.

You cannot do changes on the management account from the child account, unless that child account was assigned as a delegated administrator.

Since your goal is to reach S3 data, In my opinion is best to request access to the s3 bucket.

You would need from the payer account modify the s3 bucket policy to allow access https://repost.aws/knowledge-center/cross-account-access-s3

Another option could be cross account s3 replication: https://docs.aws.amazon.com/AmazonS3/latest/userguide/replication-walkthrough-2.html

For the two solutions referenced in the links you shared, you need to have access to the management account of the organization. Another option, if you have Business, or Enterprise On-Ramp, or an Enterprise Support plan, you can also leverage AWS Support APIs in individual accounts to refresh and push Trusted Advisor check results to a S3 bucket, and replicate the data from all individual account buckets into a common bucket.