That fence should be easy work whether you pull it down or cut it. 300' isn't much when you are pulling large sections.
$1500 should more than cover it. I think you could do it in a half day if you have good access. Figure posts every 10', that's only 30 posts. Easy work for a machine.. but that fence is worth something whether it's scrap or sold if they don't want it. Might cover some extra fuel money.
"You Can All Go to Hell, I'm Going to Texas." --Davy Crockett