AWS Workspaces + Simple AD not protected by AWS DNS Firewall

I'm working on preventing DNS exfiltration in an environment that makes use of AWS Workspaces + Simple AD. The WorkSpaces don't need to resolve anything via private hosted zones. They do connect to services hosted on an EKS cluster in the same VPC, however they have public domain names.

The Simple AD documentation reads to me that Simple AD would use our VPC's configured DNS Resolver:

Simple AD forwards DNS requests to the IP address of the Amazon-provided DNS servers for your VPC.

I have AWS Network Firewall and AWS Domain Firewall configured - the EKS clusters DNS queries are correctly being filtered. However the AWS WorkSpaces can initiate a DNS request and the request bypasses the AWS DNS Firewall entirely (a DNS server outside the environment receives the request).

Some assumptions of mine:

AWS Workspaces instances use Simple AD for configuration, and by default they use the Active Directory Domain Controller as their default DNS server. The Active Directory Controller isn't a machine we directly control, it is part of the managed simple active directory service from AWS.

What I think is happening is the Simple AD directory controller doesn't use our VPC configured resolver - and is recursively resolving the DNS query from the WorkSpace member instance. I'm assuming it isn't feasible to change the workspace instances to not use the domain controller's DNS server as they won't be able to join the domain? Is there any way of configuring the directory controller's behavior in this respect?

I tried creating an outbound DNS Resolver and associating it with the VPC via a DHCP option set, but that didn't impose our restrictions on the DNS queries coming from the Workspace instance.

The other thing I'm considering as a potential solution is upgrading from Simple AD to Microsoft AD. I understand this would provision two domain controllers within our VPC - which may be protected behind our network and dns firewall? I don't see why this would be different for Simple AD though? In any case, this AWS security blog certainly reads like MS AD can be make to work with the AWS DNS firewall - https://aws.amazon.com/blogs/security/protect-your-remote-workforce-by-using-a-managed-dns-firewall-and-network-firewall/

Appreciate any pointers!