Thank you for your reply.
Unfortunately the project requirements demand the brightest possible LED strip, so the 12V supply will be fully dedicated to powering the strip.
The LED strip is also required to be on during the servos operation - basically the LED strip needs to be on the whole time of operation.
I need one servo that can rotate 90 degrees, and another which can fully rotate 360 degrees - I have read that a sail winch servo can achieve this?