You probably do not need servo's per se, as this is really point to point positioning.
If you can find a similar device already used on automobiles that do a similar job, it might be easier to source.
For example, although a bit heavy duty, a wiper motor usually transfers rotary motion to oscilating motion, the sometime have built in limit switches.
It may be possible to use this method with flexible actuator and keep the motor out of the way and use a forward reverse action to move an arm 180 deg.
You probably just need to engage the motor one direction to a limit switch and then reverse to the second L.S.