Another starter who may be on the SOX radar is the Angels' lefty Tyler Anderson. He's 33 years old but has an 8-8 record with an ERA of 2.97 and a 1.17 WHIP.
The problem is that half of MLB teams are looking for a starter, so the sellers will be overvaluing their tradable pitching. I'm guessing that the SOX would have to include in the trade one of their top 3 prospects.
Erick Fedde of the White Sox is also obtainable, but he would probably require even more prospects because his bargain contract runs thru 2025.