Someone might say it's possible but its about as likely as finding that helpful techie at Radio Shack.That's enormous travel for a solenoid. They weaken dramatically as the stroke increases.
Yeah, a screw drive linear actuator would be much easier to source with that distance of pull...
BUT, look at power door locks for cars many of them get close to 1" of travel (they are screw driven actuators normally), with a small fixed lever on the output you could increase that to 2" and still have a good amount of torque...
This image shows how you would increase the travel using a lever...
