You've got a good idea, but you're going at it the hard way. I built this same project several years back, and it worked great!
Problem 1: Power - 1300' or so, is too far to make power for 110 VAC. Voltage drop over that distance is going to kill your motor, so, "alternative energy" is going to be the catch phrase you need to think on. Solar or Wind are the better choices in this instance. I am including 3 links on these subjects (all from the same person) which can guide you through the many steps necessary to get power to your GDO.
http://www.mdpub.com/ His home page
How I built an electricity producing wind turbine His Wind turbine build
http://www.mdpub.com/solar/index.html His solar cell build.
In these, he discusses the changing of DC power to AC power in the correct, safest, and lowest cost manner.
http://www.instructables.com has many other alternative energy resources you can read over, I found the sites above to be among the best in this area.
CAUTION: INSTRUCTABLES.COM CAN BECOME ADDICTIVE!
Problem 2: Opener sensors; most of the 'Box' stores now carry replacement sensors, and remote opener buttons (Getting your openers for free, you can afford to buy a few parts). Sensor placement; I didn't feel the need to have sensors on my gate application, so I mounted the sensors in a short piece of 1-1/2" PVC tubing (pipe) so they were facing each other (wired them up first and made sure they were working), mount the pipe anywhere convenient. Problem: SOLVED
Problem 2a: Opener buttons. simply put, buy a couple (one for each vehicle you might normally use to access the property), If you want easy access, the option of a push button is always there, and "bell wire" can be purchased in 1000' rolls usually at the Box store too. You only need 2 conductors for this (4 push buttons would be needed if you don't get any wireless opener buttons,[opening and closing, going both directions] but you would give up all security protection). 1 more button at your house would save steps or fuel if you leave the gate open, or want to open it before leaving home.
NOTE: this method negates any form of security beyond keeping animals in/out
If you are expecting others to drive through this gate, you might consider a key-pad operator mounted on a post near the driver’s side of the road
Problem 3: Operator installation. My opener was in a similar situation (outside, exposed to weather, etc.) it was a chain driven GDO. I solved this issue by putting a 1-1/2" PVC pipe over the track or rail and securing in position with 'L' brackets & protected it, and the operator, housing further by using a large ‘squarish’ plastic pail with a snap on lid. a 5 gallon round pail MAY work. (Hit a restaurant or donut shop for a square bucket, fruit fillings and veggies come in these kind of buckets with lids) The pipe has to be split to allow the connector to travel it's length. I mounted my opener inside the bucket, with the track going through the bottom ofr the bucket. this allows you to open the bucket for service or adjustment. I mounted the bucket on a steel framework made from an old real estate sign, and the other end to a smaller version of the same material.
You will have to build your own connections between the operator shaft, and the gate. (I used the swiveling connections from a load holding bar from Harbor Freight).
NOTE: Adjust the travel of the opener connection before you make the final attachment to the gate. Most GD Operators travel 7'. to open your gate as pictured, shouldn't require more than 4'-5' (if that much). I would suggest holding on to the gate and your opener bar connection, push the button to open the gate, and walk both items to check the travel. Do this in both opening and closing, then adjust until it's right. Once travel is adjusted, make the connection, and adjust closing and opening force.
That SHOULD cover everything. If you have any questions, I'll try to answer them.
My opener worked for several years until we got a dog that could escape, and I had to secure the gate better.
(It never gave me any grief once I had everything installed & adjusted). Also mine was next to my house so power wasn’t a problem.
Good luck, and keep us posted !