The plumbers showed up around 5pm on Friday night. They managed to dig out both faucets and replace one with a seriously kick-ass hydrant in an hour.
The one closest to the house, it's been broken for almost a year. Unfortunately, it was too old and rusted to fix. I was used to not having it. But I'm going to get an estimate from the plumber to see how much a brand new line would cost to install.