I think I had the same type of LED strips as you Ian.
These were the ones I got, I cut 9 off to get a good size to fit the whole cluster
I did it slightly differently though.
Drilled 3 pairs of holes in the back plate of the cluster.
Drilled an extra hole in the top to pass a draw cord down.
Drill six holes in the bottom to pass the LED strips up though.
The top showing draw string hole...
The bottom end showing the access hole.
I passed a draw cord down to the access hole, fixed on the LED strip and pulled it up, attaching the LEDs to the back plate using cable ties through the holes.
Sealed the holes with silicon, job done. Mebbe took 20 minutes for both sides.