I may be missing something but I think you can do what is proposed with VirtualBox. I use it for my virtual dev machines and run them in headless mode. For example the command:

vboxmanage startvm "Name of VM" --type=headless

to boot an image up, takes about 10 seconds to be ready to ssh into (You can ssh immediately it just waits till it has booted to connect).

vboxmanage controlvm "Name of VM" poweroff

If you want to turn it off from the outside.