Got API Gateway Lambda Configuration working after a few days of exasperation. Seems like API Gateway has a caching issue that gets into a weird state if you mess around in the console too much
Got Fargate API working. I just missed a security group on my load balancer *facepalm*. That being said, it looks expensive so I'm probably going to go serverless anyway, lol.
Still struggling with connecting to fargate tasks. Been messing around with security groups and ACLs. Haven't actually made any progress but I'm counting it.