I started with the ribbon cable, only to find that it is solid core (which will break in my design in no time). So I deciding that I needed a stranded cable, which I had to get hold of today.
In the meantime, I did a few tests with the screen and a RPI model B+, to see what performance I could get from it. At least once I have this all connected and working, I have a fighting chance of getting the software right first time!
The good news was having found the pinout for the screen, it confirmed that only 16 connections were required, not the full 26 of the existing header connection. This will save space on the wiring in the device, reduce points of failure, and save me soldering. I started soldering the wiring to the RPI GPIO, and started work on desoldering the header on the screen. This required gently separating the screen and touch layer from the controller PCB.
This all went reasonably well, however at that point, my soldering iron died. I suppose that's my fault for putting on my Christmas list an not specifying a model myself! Either way, a new one has been ordered for collection tomorrow.