If NAT Gateway is truly the reason for slowness as you're hitting the limits of throughput, have you considered having separate VPCs for each workload? Amazon WorkSpaces ideally should be in its own VPC regardless, as it is a very different workload than EC2 servers.
Slowness within the AWS (EC2 and Workspaces) in Internet browsing itself, sometimes almost impossible to access a simple website.
Using IAM Roles within AWS WorkSpaces (Windows)Accepted Answerasked 9 months ago
How to get EC2 instance to access internet facing Network Loadbalancer.asked a year ago
Slowness within the AWS (EC2 and Workspaces) in Internet browsing itself, sometimes almost impossible to access a simple website.Accepted Answer
Block Internet on Workspacesasked 4 years ago
Does Workspace use Internet from AWS or local Internet?Accepted Answerasked 7 days ago
Access to Public S3 within private subnet in VPC without Internetasked 3 years ago
Allow Lambda to Access AWS Services+VPC+Internetasked 3 months ago
My lambda function is able to access internet sometimes and times out sometimes even after configuring with NAT gatewayAccepted Answerasked 9 months ago
Client VPN slownessasked 4 months ago