Will replacing the crank & camshaft position sensors or timing chains fix P1340?

Sounds like this is not unusual to replace then. My car has 121k miles so it seems early to replace. I understand this takes an extensive amount of time to replace since they need to remove the transmission to get to the chains and tensioners. Is $3-4K (parts and labor) an average price to fix this? Is it worth it to replace this or would I be setting myself up for additional repairs?

The mileage will vary when this problem occures depending on oil change service history and driveing habits. Next what is the overall condition of car? If its falling apart might want to cut your loses. The average cost you mention is a bit high...but that too will vary depending where you are in the US and labor rates vary. If your leaning to repair just do your research and find a reputable shop that does a lot of VW work. Good luck to you.