Unable to get Recorded Queries setup to an Amazon Managed Service for Prometheus Remote Write endpoint

We have a Grafana Enterprise environment in our Amazon EKS cluster and we’ve successfully added our Amazon Managed Service for Prometheus instance as a Data Source. No problems there. But, when we go into Recorded Queries and add the Remote Write path provided by the Amazon Workspaces console (well, just the /api/v1/remote_write part as the rest of the URL is in the Datasource), we get back the following error:

expected HTTP 200 status code: actual=404, body=<HttpNotFoundException/>

Looking in the Grafana debug logs, we don’t get much more detail about this other than it adds
error=" Unprocessable Entity" remote_addr= traceID=

We’re pretty stumped as from everything we can tell, the remote_write endpoint should be enabled automatically in the AWS Prometheus instance and accessible. The Grafana EKS cluster and the Workspace where the Prometheus instance live are in the same region and we know Grafana can talk to it because the Datasource query endpoint saves and tests fine.
We’ve also double-checked that the sigv4 service role has aps:remote_write permission assigned to it.

The only thing I have found even remotely close to this issue is this post about K6 prometheus not supporting remote_write via Sigv4 yet:
K6 promethues remote write support - Grafana k6 - Grafana Labs Community Forums

Not sure if that applies here as this is Amazon Managed Prometheus from a Grafana Enterprise cluster, but google has provided me nothing else even remotely close to our issue…

Has anyone else successfully setup their Grafana Enteprise environment to send recorded queries to an Amazon Managed Service for Prometheus remote_write endpoint and, if so, what did you have to do to get it to work?

Thanks for any help you can provide.

Grafana version: 10.1.1