Check the cable for fray. The shifter is what dictates the amount of cable that is pulled. If the cable is worn it might not have the ability to pull enough cable.
Change the cable and see what happens. Its cheaper than 150$...maybe there is a small amount of damage to the cable housing that isn't so easy to spot.
The plastic bottom bracket cable guide could be slipping around from the screw it threads into. Inspect it for any signs of scrapes and wear.
Once you rule out the cable issues it could very well be the shifter. If that is the
Try the cable/housing swap.
Is the rear drop out bent?
I reckon friction is pretty spiffy too! That would cost you about 50$ for new ones.