We do it the way you re doing it all the time and at the same time of year....
when you get off the plane instead of walking straight ahead to Immigration/Baggage Claim, you will see an InTransit sign on your right and a small ticketing area where WinAir and SBC will have signs .....go there instead of immigration ....they will process you there and then you will clear security which is almost right next to the InTransit booth and voila......you re done.....walk to your gate which will be on the complete opposite side of where you will come out
couldn't be any easier or seamless the way you re doing it......typically we go from the big plane, to the gate for the small plane in 30 minutes or less