The steps you've taken are the ones available plus the use mysql-front and perform the copy database. The length of time the copy process will take will depend on the workstation from which mysql-front is running as well as the network connection/server performance.
If you can get the upgrade mysql binary from 5.0.x and run it on the same system where the database will eventually reside then run the 5.1.x upgrade version on the same.
The only thing remains is to use your application as I think DaveBaldwin may have meant that dealt with testing your application/s to make sure that it functions correctly with the 5.1.x updated database.
IMHO, trying to save time may inevitably lead to spending more time down the line.
I've seen some that had issues skipping version which are often detected later down the road.