I'm not sure the Cubs have much of a need for Teheran at this point... I'd look to the NL West for possible targets
I'm thinking the Rockies. Maybe as part of a Rockie salary dump like Teheran to Colorado for Jose Reyes, OF David Dahl, 3B McMahon and C Dom Nunez and the Rocks pay the Reyes buyout for 2018.
Braves would owe the balance of Reyes' $22M this year and all of the $22M next year. Net 2017 payroll add: $15.7M (Remove Teheran's $6.3M)
Then you go Freedie Freeman and Grilli to Cleveland for (either Napoli or Santana) plus OF Frazier, 1B Bobby Bradley. Net 2017 payroll add: -$20.5M
Then you go Olivera, Garcia and AJ to the Yankees for McCann, Headley, Ellsbury (Yanks contribute $40M), OF Judge, 3B Miguel Andujar, OF Leonardo Molina. Net 2017 payroll add: $36.5M
Then you go Markakis to Baltimore for C Chance Sisco and 1B Trey Mancini. Net 2017 payroll add: -$10.5M
Total net 2017 payroll add: $21.2M
You lose Aybar's $8.5M after 2017 (I'm doubtful you can trade him for anything)
Whatever the net is on Swisher and Bourn
SO in 2017 you have:
CF: Inciarte, M Smith, Ellsbury, Dahl
RF: Judge, Inciarte, Frazier
LF: Inciarte, Smith, Frazier, Dahl
1B: Mancini, Bradley, Judge
2B: Albies, Swanson, Peterson
SS: Reyes, Albies, Garcia
3B: Headley, Swanson, Ruiz, McMahon
C: McCann, Flowers, Nunez, Sisco
And you keep all your pitching except Teheran.
In 2018 and beyond you are looking at something like:
SS Albies
2B Swanson
CF Dahl
LF Frazier
RF Judge
3B McMahon
1B Bradley
C McCann/Flowers (with Nunez and Sisco in the wings)
SP: Newcomb, Blair, Wisler, Sims, Folty (with a large number in the wings)
RP: Viz (closer)
That takes care of your short term and allows you to payroll supplement from the 2017-18 FA market as necessary because of the minimized payroll.
Then you go best available at #3, which will probably be Groome over Senzel and follow up with best available the rest of the way. You go big in international FA with Maitan, etc. Then you pick early and often in the 2017 draft because the team sucks in 2016. Then you go low on International signing in 2017 (because you probably can't go high) and instead invest in the 2017-18 FA market.
That sets the team up short and long term with exciting young talent at the ML level and the minor league level.