Maybe call your local invisible dog fence installer and have them run the wire. A quarter mile run won't take them more than an hour? The wire self propelled wire installation gadget they use is slicker than snot. Toss a spool of wire on the thing... fire it up... and away you go. Rocks... roots... not a problem. Only issue I'm aware of is you need to use wire with a fairly stout insulation to avoid nicks in your line. The dog fence wire is two wire if I remember right.
You might be able to rent a unit? I messed around with a blade on my weed wacker for about a minute before realizing it was a rediculous attempt. Then I looked at building a hitch mounted sort of mini rollover plow for my garden tractor figuring I could flip up the sod... lay the wire and flip the sod back over on it. Then I came to my senses and called the dog fence guy and paid him to do it.
For your gate I'd think hard wired would be a better way to go?