If you're suspecting the crank is out too far, the information needed to see if there's a chainline/spindle length problem is public at si.shimano.com. Nominal chainline for this crank is 50mm with a 123mm BB. Measure the chainline. You can then compute the current spindle length without taking anything apart. You can also compare it to the FD specs on the same site to know whether the FD you have should be playing nice with either 50mm or whatever the chainline is now.
It's possible that someone put a new crank on without re-adjusting the limit screws and cable anchor position from scratch, which in most cases will not work unless it's a like for like crank replacement.
If the chainline is good or really if it's anywhere between about 47mm and 52mm, and if by tightening the cable "too much" you mean to say that the problem you're running into is literally running out of barrel adjuster adjuster, then the first thing to do is loosen the cable anchor, put the barrel adjuster back in all the way, confirm the FD position and limit screw setup is good and correct it if it's not, then anchor the cable and re-adjust the FD. The way the question is written, it's unclear whether these normal FD setup steps have been taken or not - if not, the best thing in any case would be do these setup steps from scratch and seeing if it works before looking for a deeper problem, unless the chainline is way off.