Not to leave you guys hanging about my specific case, the process we do is as almost as automated as possible. All the heavy lifting is scripted and the deployment to all other environments is done via a single click, however for prod we do have an additional checks, as deploying the wrong build could have some bad consequences.
I use a similar system when deploying builds to production. The deployment itself is a multi-step process where I have to pick out two artifacts, verify that their git commit hashes are correct, then pick out the correct jenkins jobs and run them in a specific order (providing artifact numbers as input). At every stage I point to my screen, read out the information and only click on things that I'm pointing at. This may be anecdotal but multiple times I have stopped myself from clicking on the wrong thing only after saying its name out loud.