Check out ShotMarker. They say: "The Sensor Hub battery lasts 100 hours, and the Access Point battery lasts 18 hours". All rechargeable.
They say its designed for F-class, but I could not find on their website a statement for the maximum range for the transmitter. F-class is max 1000m. Maybe give them a call at ShotMarker to see if can work for 2,000m?
I know nothing about this technology, having not used it. But I see YT videos of it being used for F-class training. Reason I am interested is that if this 2000m range is a go, I might travel out on vacation for the opportunity to shoot 2000m, which is way way impossible where I live. It would be awesome.