I think you need to go all in now with the expectation of having a 3 year window. The White Sox don’t have endless financial resources but they should be able to push a $150 million payroll over the next 3 years. Here is what I would do if I was GM -
Trade for Lindor and extend contract, move TA to LF. Looking at the package BOS got for Betts I think the price for Lindor would be less than what LAD paid.
Sign Springer
Sign Stroman
Acquire TOR arm for a package built around Vaughn
This lineup would be the best in baseball:
TA
Lindor
Robert
Abreu
Moncada
Jimenez - Permanent DH
Springer
Grandal
Madigral
Rotation would look like:
Giolito
TOR acquired via trade
DK
Stroman
One of the remaining arms you didn't trade (Kopech, Dunning, Cease)