Eels will certainly climb, and the smaller ones seem to just keep going untill they run out of water. Where I grew up was in on the border of Egmont Nat. Park, also about 300m. The small streams there were full of young eels, 15-30cm long. Very shy, you would only find them by flipping over rocks and poking under logs. Water falls are no obstacle to them, give them a nice wet night and they just go overland. We found them above a 10m waterfall at my old farm. Maybe they did overland, but that would be 500m down the road.
I live in Stratford, also 300m asl. We have 3 semi-tame eels in the back yard, around 1m long, in a stream that you could jump across with a good run-up.
Try feeding your one at dusk. They can get very tame over time and will hand feed once they get used to you. Some raw chicken or beef offcuts will get their attention. Eels are very long lived and you may have the same ones coming to feed for 20-30 years.
Ian