Thanks to everyone who contributed to this thread. I wish I'd thought about Todd Stock's suggestion of making a dummy at the same time, but it was half done by then. Next time...
I basically followed Shane's advice of inlaying the ring first, using Titebond and then cutting the grooves for three strips of veneer inside and out and flooding these with CA. I cut these two channels with a 1/16" dia. Stewmac downcut bit. I cut a trial channel in a piece of scrap and adjusted my veneers to fit. The thickness of the black veneers seems to vary in the finished rosette. I think the reason for this is that when I cut the two channels, the Titebond burned onto the bit and the resulting channels were a bit wider than the trial. Because of the added difficulty of inlaying veneers and trying to get a continuous ring without a visible join, I didn't notice that the groove was a bit too wide. The CA filled up the gaps and makes it look as if the black veneer varies in thickness. You can also see the joins if you look for them , even so, I'm fairly satisfied with this one. The next one should be perfect.

I'll perhaps make a Wells/Karol jig before then though.
Click on the pics for a better image.