I believe the White Sox could offer the exact same total dollars, AAV, and opt outs as the Yankees and still present the more attractive option. Let's use your $330 million example, and assume a 10 year contract with opt outs after years 3, 6, and 7. If these are the offers:
Yankees: 33-33-33-/-33-33-33-/-33-/-33-33-33
White Sox: 45-45-45-/-45-45-40-/-35-/-12-10-8
It's the same dollars, opt outs, and AAV, but Machado would be stupid to take the Yankees offer at that point. Hahn needs to be creative and use the payroll flexibility the rebuild has afforded him to land one of these big fish and ensure they opt out when it's best for the team.