Questions on Hiding Led Wire in a Driftwood Piece

First of all I'm very new to this, so don't hesitate to suggest seemingly obvious solutions.

I'm looking at creating a driftwood piece inspired by Andy Thomas. Hover over the middle of image with the "bubbles" of light.

My hope is to embed some RGB lighting in the wood itself. My initial intent is to use some RGB LED strip. Ideally, I conceal this under the surface of the wood and drill holes to reveal the light underneath.

Some thoughts:

1. Drill a series of holes where I plan to reveal the leds. Then cut a series of intersecting cuts using a Dremel rotary tool + cutting wheel to release a channel of wood. E.g. -/. Proceed to carve out some additional space in the revealed wood. Place the led wire. Replace the excised wood.

2. Use something like a keyhole bit to carve a channel in the wood and slide the led wire through it.

There's some gotchas with this. Neither of these cuts would be straight and would need to follow the contours of the wood. With the first option I'd want to avoid a series of inadvertent arcs from the rotary tool tracking off course. The shape doesn't really lend itself to a jig.

The keyhole bit would be interesting but bits I've seen leave a hole that's too large. I wouldn't want anything larger than 1/8". These also tend not to be very deep - at points I may break out through the surface and damage the piece.

One final though I had is that I could use my Dremel to route out a 1/16" groove in the piece and place the led strip parallel with the groove's sides. This might also be easier to freehand. I don't see Dremel offering a router bit this small but I might be able to find one from a third party.