Originally Posted by
anabolism
With Global Entry, you should be fine. Clear immigration and customs in T4 (which, with GE, shouldn't be too bad), exit to the street, walk over to T4 (just a few minutes). If your AA BPs for your Eagle flight don't show TSA Pre-Check, stop at the AA desk in T4 and get new BPs that do. Then head upstairs to the Pre-Check line (all the way to the left), and you should be inside quickly. You can take the bus from T4 Gate 44 to the Eagle's Nest.
Another alternative to re-enter airside is to just the stay in TBIT and use the little known security checkpoint between TBIT and T4. There is rarely anyone in line. Although there is no formal PreCheck, PreCheck Lite is available. You can find it by using the right customs exit and then another right after you exit the baggage drop area.