What I’m Looking for
We’re looking for a Git host that has web-manageable deployments via Git. Most deployment software I’ve found uses FTP, and if there is an update made on the live server (some of our scripts generate occasional code changes) the FTP seems to blow away the live changes if the Repository has the same modified file (what would otherwise be a merge conflict). We’ve tried beanstalk, springloops and deployhq.
Current Workflow
We currently have a cumbersome deployment process which involves committing the live code and pushing it to the Git server, then pulling to a developer machine, resolving any merge conflicts, then pushing back to the Git Server, then pull to the Live server.
Does anyone know of a service that can do differential deployments via Git, that may not deploy if there is a merge conflict, and just warn about the difference? This may be a Git Hosting service itself as well.
Update
I made this infographic to help display our current workflow, and how we’d like to have our workflow:

See my answer below for a git-based deployment strategy that we use daily.
It deploys to a fresh directory each update, so it will never have merge conflicts on the server. I strongly recommend against editing deployed code, but to each his own.
This isn’t a hosting service however, it’s do it yourself. Thus it doesn’t quite answer your question, but it’s worth noting.