OK here you go (idea):
I am on record as wanting to build in a different way. But, if the Braves just have to trade for SP, then:
Detroit trades Braves: Fullmer, Verlander, Zimmerman and Kinsler. 2018 add payroll (~$63M) then Kinsler goes away (-$10M) for 2019, Verlander goes away (-$28M) in 2020, Zimmerman goes away (-$25M) in 2021.
Detroit severely cuts payroll and the sugar to make it happen is Fullmer.
Braves trade Detroit: Kemp (+$16M) through 2019, Camargo (plays second for Kinsler), Markakis (+10.5M) through 2018, Pache, Sims, Sanchez, Wisler
Detroit begins to clear up its long term payroll and rids itself of Zimmerman (Verlander they could at least give away). Braves take on quite a bit of money but get their veteran arms short term ($53M per year as opposed to typical yearly veteran arm expenditure of $15M~$30M), buy some time for the youngsters to develop and get a very good, young, controllable starter in return without having to give up much. Kinsler gives you a legit veteran to help man 3B and/or 2B in 2018 after which he is gone.
Braves then trade Adams and Teheran for best available prospect package. Decline Dickey's option.
2018 rotation: Verlander, Fullmer, Folty, Newcomb, Zimmerman (let's you go slow with Allard, Soroka, etc.) Hope the return to the NL brings back Zimmerman to a solid #3.
2019 rotation: Verlander, Fullmer, Newcomb, Zimmerman, best of Allard/Soroka (Trade Folty before he get's too expensive)
2020 rotation: Fullmer, Newcomb, Allard, Soroka, Zimmerman
2021 rotation: Newcomb, Allard, Soroka,Wright, Anderson (trade Fullmer before he get's too expensive)
2018 with Kemp and Markakis gone you play Acuna on one corner and fill the other through trade acquisition (maybe from the departure of Teheran and Adams).
Not saying I would do it. But, an option if you MUST try to add veteran pitching to "compete" in 2018.