Tiling spade is how you get in like biff said. We had a probe to find the least distance - 1/2" sharpened rebar works. Usually the shortest distance is opposite the run - which is the slanted 'point' to the ice. It is important to seal the house with some wet silage to keep it from freezing or they will abandon.
Open water is a lot more efficient. You set a trap in the water on the little shelf on the south side of the house with a fixed chain to the anchor. We used a lathe. So when the rat gets into the trap and swims around the stake it can not get back to the hut. The weight of the trap will drown them.
Back in the late 70's we got around $8 for skinned, dryed, and graded hides. Pretty good money for the volumn we did. Five sounds like the market is back - should be able to add a couple for skinning and drying.