If you're arriving into T4, just go directly to the Admiral's Club and depart for TBIT when you feel comfortable with respect to your flight time, and if necessary, check-in time with SWISS. Hopefully, you have just one itinerary so you're already checked in for your SWISS flight w/BP in hand when you arrive into T4.
If you're arriving into T3, have a fully refundable ticket purchased or an itinerary printed for a same-day AA flight. You can show that to the "security" person at T3 who will let you take the airside shuttle bus to T4. The one-way T3 to T4 transfer takes 10-15 minutes with a stop and possible bus change at the American Eagle terminal. However, you can remain airside with no unnecessary security checks.
If you're arriving into any other terminal, your best bet is to buy a fully-refundable ticket for an AA flight departing from T4. Address any check-in or luggage issues with SWISS prior to going to the Admirals Club.