Compaction and water restrictions (due to play/practice start and end of day times, municipal etc.) will probably factor more into your turf health than the PH. Hell, we've got gray clay with actual salt deposits on the surface in some fields, including golf, and still able to keep grass going just fine.
Focus on keeping it open and as deep as they'll let you and mulch mow everything back in to give some padding, bulk your organics and extend your fert apps.
Ammonium sulfate will boost your sulfur in the soil profile just as quick, if not more so, than a SCU (depending on percentages). Ask your local supplier, soil conservation specialist or local extension office.
"an odd deal where they weren't happy with trugreen" made me snort laugh, so thank you for that..lol