Complete Azure deployment takes a while for a reason, but here's what I do.
I stop the deployment, then while it is in "stopped" state I click "upgrade" and choose the service package. The deployment gets into "upgrading" state and it takes up to three minutes to complete and after that it gets into "stopped" state. I have to click "start" and wait for several more minutes to start the deployment.
I don't get it. The deployment doesn't need to be stopped prior to upgrading - it is already stopped. The deployment isn't started after upgrading. What is taking three minutes then?