We did this and I still haven't shipped over the rest of our stuff. We moved with two suitcases, a medium Home Depot box, a duffel, and two other carryons (and two cats but they were a different issue).
What I did since we had a large enough house was to set up one room that was the Packing Room so I could see what I had set aside. So the luggage I knew we were taking was in there, and while I packed up the rest of the house, I would move things into that room that I thought I would want/need right away on the trip over, By having the separate room I could see immediately how much I had, how much space, not misplace stuff, etc. I could also think on what I had chosen and always go back and swap things in and out while I was packing up the rest.
For the rest of our stuff we set up the bigger boxes in the basement - kitchen extraneous, sports, non-needed clothes, etc which, while it wasn't fun running up and down the stairs all the time, again gave me a place where I could make a mess and pack stuff and sort without tearing up the whole house. It also allowed us to start selling our furniture from the first floor without people crawling all over boxes.
What you could also do is tape out the space of the container you are shipping. My mother used to do this on our very long haul moves to Alaska, so she could see the exact space.
Our method worked pretty good, although we were still up at 3 am throwing things out and packing the U-Haul, but it was fairly low stress. Granted, I did have a bit longer than you, but it was a divide and conquer strategy! Now all our stuff is in my parent's basement waiting for this summer when we can hopefully finally UPak it to the UK, but its all ready to go for the most part.
