Pocket cameras have come to have much better resolution than expensive binoculars. As an example my Nikon Coolpix S7000 with 20X optical zoom and superb anti-shake technology will bring very distant objects into sharp resolution. You can also make use of its additional digital zoom. I had been having trouble reading the eartag numbers on our sheep to record their lambing details. I had bought a new pair of 12X binox, even a 16X monocular but they are completely surpassed by my camera – and it is so easy.
Instead of glassing those distant slopes with a pair of heavy binox you should try a pocket digital camera. Mine weighs 160 grams including battery and SD card. I notice Sony now have a new pocket model with 30X zoom and still under 240 grams! You can make up an adapter to slip into the barrel of your gun to enhance stability so you can sit and glass the opposite hillside, or you can use a couple of rubber bands (see photos – the adapter on the right needs a nut to tighten the rubber tubing so it is firm in the barrel). See: http://briangreen.net/2011/07/trekking-pole-camera-mounts.html