Go straight to TBIT. It's not an issue whatsoever, you won't be denied at the main TBIT security. I've done it for this flight more than once, and actually it isn't too busy in the AM in my experience.

The downstairs TBIT security which leads to the T4-TBIT corridor seems to require an AA BP now unfortunately, but upstairs is fine.

TBIT doesn't have a lounge accessible to DL elites, so the only reason to go to T2/T3 would be if you have lots of time and want to go to the SkyClub. But the bus ride is annoying