First off, it's unlikely they all suck, but let's assume they all do.
The current obligations for the 2017 Red Sox amount to 148 million, with Ortiz retiring, Uehara leaving, Buchholz leaving, Hanigan leaving, and Tazawa leaving.
Castillo has options, so he stays in the minors. Porcello moves to the BP in a swingman role, and the one of Panda/Hanley who sucks less stays, the other is cut/traded eating most of his salary (the Sox have eaten big contracts before, so it's safe to assume they would now). Assuming a 190 million soft cap, 10 million in arb raises, and holes in the outfield, 1st or third, the BP and the rotation, this is what a Red Sox offseason MAY look like:
C Cristian Vasquez
1B Sam Travis
2B Dustin Pedroia
3B Travis Shaw
SS Xander Bogaerts
LF Andrew Benintendi/Yoan Moncada
CF Jackie Bradley Jr
RF Mookie Betts
DH Hanley Ramirez
SP
David Price
Eduardo Rodriguez
FA/trade (3/45, options include Buch himself, depending on his platform year, Doug Fister, CJ Wilson, Andrew Cashner, Jesse Chavez, etc)
Joe Kelly
(Battle between Porcello, Wright, Brian J, Henry Owens, etc)
RP
Craig Kimbrel
Carson Smith
(LH setup man from FA, options include Brian Matusz, Eric O'Flaherty, Manny Parra at 3/18)
Matt Barrnes
Tommy Layne/Robbie Ross Jr
Noe Ramirez/Brandon Workman/winner of ST battle
Rick Porcello
Bench:
Blake Swihart (backup catcher, they have him learn other positions)
Brock Holt
Chris Young
(FA 1B/OF like Garret Jones)
That's around a 183 million payroll, and a possible contender, health permitting. That's just my take on it, and obviously it's just a fantasy scenario, but it proves that the Sox aren't "clogged" anywhere. At all.