I like Burl's idea, if you have a
tractor... There's a
fence supply near me that also rents equipment, could be worth looking into.
I'm trying to guess at the bulk of the cable... 10/3 what? UF cable? with a ground conductor? or round rubber jacketed stuff like SJ cable? 1000 feet of 10/3 is more than you want to lift for sure.
Maybe you can get an empty reel from an electrical supply house? or a telephone/internet company? (There's some empty reels in my neighborhood on Craigslist, only 3000 miles away!)
It sounds as if it is laying on the ground? or overhead and could be on the ground? in which case you could bring the reel to the uphill end and roll the reel over the cable towards the downhill end, gathering the cable as you go.
Maybe you could pull from one end, but risk damaging it in many ways and no way to watch the entire length.
You might also make some measurements while it is laid out (if there's no markings already on the cable) for approximately what you are going to take for your
project. For that matter, two smaller reels might be handy, one for your piece from one end, and the second reel for his piece from the other end.