That would be the logical answer, but I was just concerned that ST rules may not be logical. It sounds like I should get access to KE, but I guess I will ultimately be at the mercy of the lounge dragon. The flight is on DL (AM only flies to MEX, not CUN).

I usually fly *A and am *G. I think nothing of walking between T7 and TBIT for lounge access (*A lounge for UA flights/Polaris for *A in J), so going between TBIT and T3 is certainly not an issue. I quite enjoy getting a little exercise in before a long flight. I would go directly from bag drop in T3 to security in TBIT, so no need for the bus when going to the lounge. When returning to T3, if the bus is not convenient, I can just go landside for the short walk. With TSA Pre and Clear, security is hardly a concern.