You had some interesting problems on offense, but the major problems were these:
1. Ortiz is gone. He was a prime performer at his exit with a 1+OPS and 30+HR power. Ortiz made the lineup move and had a ripple effect through it with guys getting more pitches to hit in front of him and guys getting more opportunities behind him
2. Pedroia isn't healthy. Pedey playing about 100 games necessitated getting Nunez. Also, you saw a drop of about 75 points in OPS at the position for the sox from 16 to 17. With Pedey being a shell of himself, the defense and power suffered at the position, and his spot in the lineup was typically #2, which meant similar OBP, but less guys in scoring position (or who have scored) due to the lack of power and EBH's.
3. Hanley was abysmal with runners on. Last year, he had a .875OPS with runners on. This year, it was .648. That's over a 200 point drop in a player hitting in the middle of the order.
The bottom line is, your big bopper left and was replaced by a guy who didn't have the goods to be a run producer. Pedey got hurt and wasn't the same. The lineup being without the big bat led to slight, but significant change in fastball percentage to Betts and a significant increase in sliders, which neutralized his effectiveness. He actually swung a lot less and it led to a higher walk rate, but a lower power output and a lower BA. His improved patience didn't lead to being more selective and hence higher line drives, quite the opposite actually. His LD% dropped 3% and his infield popup rate rose 3%.
The FO thought you could elevate Betts to being the focal point and they were wrong. You must add a big bat to smooth out the discontinuity in the lineup