Small electric actuator suggestions? Need something fast and programmable!

Right now I'm using a cable actuator for a prop. A small lever controls the cable, which activates any one of 7-8 functions. The problem is, the lever has to be moved by hand so I am constantly having to go and change it myself. I want to be able to control it on a number of different principles, such as a timer, a photocell, sound activated, etc.

The problem with the speed is that if the cable is in between 2 positions for any amount of time, it pops a breaker. I don't have nearly enough money to redo the entire setup. The cable actuator and things that it control are rather complex (its an OLD large robot prop that I bought from a company that was doing haunted houses and went under).

The lever itself is less than a foot long, but only moves the actual cable 1/4-1/2" when clicked into a different position. I need to be able to set it to change functions every 10 mins, or when it gets darker outside, or in a pattern that I decide. Arduino is perfect for this.

2-4" per second would be ideal, and would only need a maximum stroke of probably 3" (I need to go measure). I know of a company that was making small linear actuators capable of doing this. They've been doing similar functions (cable actuation) in other hobbys at the stroke/speed I want, but they are $1200 for the setup and they won't provide a part number for the actuator they are using when I asked.

I found these linear actuators, which are MORE than enough. The main problem is length. for the 4" stroke version, I'm looking at 17.5" extended (the other company is using something probably 6-8" extended). 9" per second speed. $150 isn't really out of the price range. Is something like this able to extend to a very specific position through something like PWM?