If I remember rightly, it's little more than a scarf knot, the cincture rope itself is knotted first with the drop end (a form of heaving knot) and then with a series of bottle knots around one end to represent the vows taken. That implicitly doubles the cincture and leaves a bight for the ends to pass through.
That, however, is an RC approach, and I tend to think a Camberian cinture might be a tad more military, so some form of lanyard, whilst remaining functional, ie easy to do up and remove. Your description of unlaying two existing cinctures gives me a clue: your problem lies in that they were pre-twisted in being laid up in the first place, and in separating them you undid the twist which was holding them close. It should be in the opposite direction to the twist in the strand. If you clamp one end and start twisting each, you'll see the cords start to lie up against each other and a new rope form.
At that point, you're talking about a rope and an eye can be formed in a rope, particularly if you're forming stopper knots. What you might do is form a thumb knot in red around the blue as a core, then butting a thumb knot in blue formed around the red, and again red around the blue. Leaving the two unlaid for a short distance, say an inch, before repeating the knots as the foundation to continue the laying-up creates an eye, and an eye serves as well, indeed better, than the bight in a classical cincture. A series of eyes can interlock each other >----o-o-o--------o-o-o----===. (This is actually a standard military engineer's lashing rope).
