I have no idea on what might be available (I'm particularly curious if you already have PreCheck externally...e.g. via Nexus/Global Entry).
One practical question: Depending on when you're traveling, if you're at a lousy time (e.g. peak hours, near a holiday, etc.) and/or are worried about making it to the airport in time (likely as a side-effect of the aforementioned) could you book a throwaway ticket on another airline (SY being the best candidate for T4) and use that ticket to clear security?