Hi @Matt 
Your Forest Admin backend is nothing more, nothing less than a nodeJS application.
You can deploy it anywhere really. In AWS, both EC2 instances and ECS (docker container) can be used. Your tech team can even go serverless with an AWS Lambda function.
Amplify? I’m not sure, I believe it’s for hosting static websites.
Should your team go for AWS EC2, here’s our complete guide 
How to deploy to Ubuntu Server
As for your side note, we’re extremely happy to have people like you go down the rabbit hole and can only celebrate all the things you’ve learned thus far with us 
We’re sure your tech team will appreciate all the heavy lifting you’ve done!