Back from midsummer. It was fun.
I don't want to speculate too much on whether or how a reflector improves the viewing of Lippmann plates. I haven't made or viewed them, and it seems impertinent to lecture to those of you who have. Kudos for giving this a go.
However, basic physics can help to understand why some things work and others do not. For example, if you want a strong reflection at the surface of the emulsion you need to provide a sharp mismatch in the refractive index.
Metals do this for free. This isn't the place to learn about refractive indices in metals, but in short, for light below a certain frequency, usually in the UV, metals have zero or very low real refractive indices. That means the refractive index difference is similar to the refractive index of gelatin, around 1.5.
Transparent materials like glass and air mostly have refractive indices between 1 and 2. To get an index mismatch as large as that between gelatin and a metal you would need to get up to 3 or more, and even diamond is only 2.5. The highest index oils for immersion microscopy are around 1.8-1.9. There are materials with higher indices, such as most semiconductors, but they absorb too much to be useful as mirrors. Basically, any non-metallic reflector is going to give you a much weaker reflection.
One reason the interference in a Lippmann plate is weak is that your light is incoherent. A laser can fill a thick emulsion with fringes, but incoherent light does much worse, even if it is filtered to be monochromatic. A rough rule of thumb for thermal light (black body radiation, aka sunlight) is that the coherence length is of the order of the centre wavelength. In layman's terms that means you can only expect to get two or three fringes. It's one reason why Lippmann emulsions are thin: there is no benefit to a thicker emulsion, it just wastes silver and absorbs and scatters light.
You can probably maximise your chances of getting good fringes by reducing the range of angles at which the light strikes the emulsion. Smaller f-numbers are the easiest way to do this, but retrofocus or more exotic telecentric designs will help too.
FWIW, the Morpho butterfly scales are 3D on the nanoscale. The remarkable thing about the Morphos is not that they have lovely colours, but that their colour is so strong, and so pure, over a wide range of angles and lighting conditions. If you could somehow reproduce their method of generating colour, and vary it across a substrate, you would be a very happy camper indeed.