If you really want a backlit backsplash, how about using edge lit glass or EL panels behind glass?

The wiring will be interesting.

If the rear of the range will also be back lit, acrylic may not be such a good material.

LED panels or EL lighting can be used under the cabinets.

EL lighting is probably less viable due to the amount of light produced and most are still non white.

You may want to talk to Helen of everlumen. Let me know.

Here is a link that might be useful: everlumen