EKS also seems like a good option here. I was actually just looking into the exact same question OP asked and I'm thinking about getting one up and running on EKS to take advantage of Autoscaling Groups

I was thinking along the lines of a deployment platform that would be scalable as it seems there have been reports of scaling issues recently. (Un)fortunately I work on Kubernetes all day every day for my work so the complexity isn't the main issue, it's just carving out some time to work on it.