If you don't have any checked luggage you can check in online, print your boarding pass, and then enjoy TBIT at your leisure. Same with coming in on another airline that has an interline baggage arrangement with OZ or if it's on the same ticket. If that one arrives in T4, T5, T6, T7, or T8 then you can just use the tunnel and skip a second pass through the TSA (with no PreCheck). If you're not worried about leaving your bags with whichever airline you're flying in then you can head over to TBIT through the tunnel and hang out until around 8:00 go get you checked bags, check in and head back to the lounge.

If not any of those options work then you need check in with OZ when they open up for your flight, usually around 8:30 pm. Given your in F they're very likely to let you check your bags if you make it before they close down for the early flight.