I pondered this for a few minutes. I had the following thoughts -- no answers, but thoughts!
I wonder if the actuators you've chosen have enough guts to move to blast gates. Mine were always kinda sticky; maybe it's okay because they're geared down, and maybe your gates are better than mine (!), but were it me, I think I'd do some tests with a fish scale or something before I spent money for six of those. (As I said... just a thought!)
If the problem was something simple like... turning on a light, it would be pretty easy to wire it up with relays. On/off/on/off, simple. But then I assume the actuators can't turn themselves off when they get to the end -- we need gizmos to do that. So we need:
- On closing direction
- Off closing direction
- On opening direction
- Off opening direction
and suddenly the relay logic and switching states get more complicated. This actuator-actuating logic sits alongside the three-position user-interface switch.
I think the project is intriguing, and not as simple as it might seem on the surface. I think using actual wires is a reasonable alternative to current-sensing; when the motor's switch is on, there is a 120v available that isn't available otherwise, and it could be used as a master "on" signal -- it could open a relay that turns on the 12 volts (which you're going to have to get from somewhere... right?).
Then there's switching and relay logic, and I suppose it could be solid-state relays (though I've never used those, and I do understand (cheap surplus) hardware relays). But in any case, it looks like limit switches are going to be required, so overall, the actuator can only run until it hits the end. And then there's some direction-switching to take care of, which I assume is a matter of the polarity of the voltage feeding the actuator. The three-position user-interface switch is easy, with a little bit of inverted logic (off is on).
There are other ways to frame the design, i.e. just put a button on each side, and push it when you want that gate open. That signal could be used to close the other one. I don't think you have to worry about any connections between the machines; just turn the other ones off if you don't want to use them. (I am a little confused about wanting two of them open on the same machine, but I guess that's for something like going back and forth or something.)
Some things will require some more thinking. Are you sure you want to do it this way? Since "simple is good," there might be ways to redo the design to make it easier to implement. I think I'd start with figuring out how to have a button that opens the gate without the actuator motor running off the end of its track. Then thinking about the logic, which is easy but complicated.