This might be a dumb question, but how is an array coaxial still really coaxial? It doesn't look that much different than a ring light, other than it appears to be bouncing the light off of a mirror (I'm not sure that would provide much benefit). The whole point of coaxial lighting is that the light is emitted down the lens axis, so the light comes straight back into the lens. If the light bounces off the board at an angle, you've lost the property of a coaxial light that makes it so desirable.
I get what you are trying to achieve, and I wonder if instead it could be done by lensing the LED light source so that it is more focused at the beam splitter surface, but then diverges afterwards. That should allow it to light a larger area, if the focal length of the lens is picked appropriately.