Sewer line repair - most cost effective method?
Pipe replacement is the most costly, but it's also the most permanent. There are (at least) two ways to replace the pipe, and you may not have considered the second method I'll mention.

The traditional method is an open trench stretching the full length from the house to the sewer main, probably somewhere in the middle of the street. This is both slow and high-impact to the surrounding landscape.

An alternative method, less commonly known to homeowners, is pipe bursting. This often requires access holes be dug only at the two ends of the pipe. A steel cable is fed through the pipe. A splitting wedge and replacement pipe, often semi-flexible HDPE tube, are attached to one end of the steel cable. A hydraulic machine pulls the other end of the cable. The splitting wedge breaks the original pipe into pieces, forcing them outward and reaming the space large enough for the new HDPE pipe to follow through. The replacement pipe can even have larger diameter than the original if needed.

Pipe bursting gets the job done with much less impact to the surroundings and often in less time. Cost compared to the other options will vary by market, but it's worth at least evaluating as one of your options.