Wanting light to run from front to back, I decided a wooden holder could be fabricated to hold the LED's. Checking what I had in the garage, a 1" slice from the edge of a length of studding looked about the right size. A 0.5" x 0.25" channel was routed into the wood on one side (for the LED's) and a 0.25" x 0.15" channel on the other side for the wires.
The wood was sprayed black and allowed to dry. Holes were drilled for the wires to pass through. Black silicon was spread inside the 0.5" channel and the LED strips were tapped into place (it's a fairly tight fit and they may well stay in place without the silicon).
On the reverse side, the wires were soldered together and heat-shrink was used over the joints. The wires were tacked into place with a hot-glue gun.
On the LED side, black silicon was used to fill the gaps between the strips.
The channel going into the wood:

Painting the wood - primer:

LED's in place with silicon between the strips (note that the silicon hides the wires which go through a hole to the back):

The wiring on the back, showing wires glued into place and heat-shrink over the soldered joint:


View of finished item:















