Just to add my own 0.02$, with a self leveling free pour epoxy like Mike suggested I'd go,with the taping the underside as well. I'd use the wider packaging tape, single strip per scale, with scale centered on the tape lengthwise. Tape it down well to the edges, then brush the remaining exposed tape around the scale perimeter, gently bending it away from the scale with your fingertip, on its exposed sticky surface, to allow the epoxy to flow off the scale and down the tape 'slopes' away from the scale as it's held off the work surface. Don't want it to pool along the scale edge before it cures..
This way the edge thickness will not be an issue post cure and with your handy files and a little time, beautiful results to an already awesome looking project.
Hope that makes sense.
Good luck..

And regarding wedge material, a nice slice of bone would work well with the abalone I think.
Look forward to the results!