Being able to just ssh into a machine is one of the problems that we did solve with containers. We didn't want to allow anyone to SSH into a machine and change state. Everything must come from a well define state checked into version control. That's where containers did help us a lot.
Not sure what you mean with lingering containers. Do you launch yours through SSH manually? That's terrible. We had automation that would launch containers for us. Also we had monitoring that did notify us of any discrepancies between intended and actuated state.
Maybe containers aren't the right tool for your usecase - but I wouldn't want to work with your setup.
Btw. most of this is possible with VMs, too. So if you prefer normal GCE / EC2 VMs over containers that's fine, too. But then please build the images from checked in configuration using e.g. Packer and don't SSH into them at all.