I've used k8s on an early phase project I later moved off from so I don't have much experience with it but I got the impression that simple scenarios worked like documented. You already had a docker based stack so it sounds like hosted k8s shouldn't be that far off from what you were running.

What issues did you encounter ? I had to spend a week working through it to get familiar with everything but I wasn't experienced with docker previously (I've played with it a few times but never had to setup stuff like custom registry, versioning, etc.)

I did end up in situations where the cluster was FUBAR but I eventually figured out that everyone just recommends rebuilding the cluster over diagnosing random stuff that went wrong during development.