Just did this last fall. If it is broken at the shut off, you don't have to replace all the way to the meter. I bought 18" of 3/4 K line and compression fittings. Have they turned the water off at the shutoff to see what side it is leaking on? If you can still hear or see water running when off it is the City side and should be there responsibility. Hardest part of mine was it was 7 feet down and back filled with rock and sand. I went and got some sand to fill the hole after I was done. And as a side note, most water providers in Michigan only cover the street side shut off. If it breaks anywhere on the owners side, it is the homeowners problem.
The barrels and torpedo heater work surprisingly well.