I used to have the GTO opener at one place in Florida, it was only 400 feet away, though. I ran 120v to it, then used a 12v power supply there at the gate plus a battery. Once you have power going to the gate area, you can use those simple plug in intercoms that use the ground wire of the 120v line as the antenna. That worked fine for us.
My next place had 2200 feet to the drive. I ran 12gauge UF wire with 2 splices put in pvc pipe and sealed with lots of silicone before burying. The voltage drop was substantial, but it worked fine to power a battery charger, and could have easily powered a 12v regulated supply. In my case, I went to an old school relay style opener that is heavy duty and had a Crown Jewel keypad put in at the same time. It has been over 13 years and still works fine. I use the power to drive a battery charger, have a deep cycle battery there in an enclosure, then run a 2000w inverter. This gives me a steady 120 volts. Otherwise, I would have a big drop under load because of the distance.
On my GTO-style opener, I had 2 board failures due to lightning, and the opener mechanism was basically the same actuator that I used on my first large satellite antenna. If you need a cheap replacement, try Burden's Surplus
Surplus Center - 30" STROKE 230 LB 12 VDC LINEAR ACTUATOR for $89, but you would need external limit switches, or use the motor, maybe? May or may not fit the bill.....
At my very first farm, I made the gate opener out of a garage door opener that used a nylon tape running in an aluminum extrusion, as opposed to the more common chain drive ones. It worked fine when I sold the place, although it was geared a little high for the purpose, maybe.
Overall, I like the solar idea, but would add to use a regulator to add life to the battery, since any panel can overcharge if it just has a diode. If I had to do it all over, I might go for Soundguy's setup, but with a sensing wire on the inside of the fenced area to automatically open as you leave.
