We just went through this. Very hectic at immigration. Dunno if it applies to you but a couple of things that helped us. We did luggage forwarding. It really helped and they did a great job. Coming through customs picking up our suit cases we grabbed a porter. Doing that gets you through quicker because the agent works with the porter to get you the front of the line. Then whilst on board we booked a private car to the airport through Cunard and it was wonderful. All the arrangements were efficient and all went very smoothly. Obviously this was all extra cost but we found it all worth the extra.