Today we decided to bridge the gap. So three of us got the canoe and put it on the ice, and got in. We tried to skootch the canoe along the ice, but that was unsatisfactory, so we got out, fetched sharp pointed shovels, and started pushing with those. It was a lot of work, but eventually we did succeed. First, we had gotten about 75 feet of rope, tied to the shore and to the canoe. Our thinking was that we might be able to use the rope to help us return. Unfortunately it seemed that the ice was actually about 80 feet wide, and so when we got to almost the end, and the canoe had finally broken through into water so our paddles would be useful, we couldn't go anywhere because the canoe was tied up! We wanted the rope clearly beyond the ice limit, but there were a few spare pieces of rope attached to the canoe and we were able to lengthen our tether, with only a little bit of nervous tipping back and forth.
We were free! Out in the open water, able to go anywhere we wanted! Except, of course, to the shore, which was protected by an ice shelf it seems the entire circumference of the lake. We paddled across and back, startling a flock of seagulls which were basking in the sun on the ice shelf. Canoeing in February! What fun!
When we returned, we tried to aim directly for the little notch we had made in the shelf on our exit and ram it, in the hopes of breaking a little more ice with little effort. We also wanted to be able to grab the end of the rope. This worked pretty well, and we recovered the rope. Now we weren't quite sure what to do, but we each grabbed the rope in tug-of-war fashion and started pulling. It worked totally excellently! We just flew across the ice, breaking it for about 40 feet until it was thick enough that the canoe slid up on top, and we continued to make our speedy progress until we fetched up upon the actual shore.
What amazing hack value. It was a lot of work to get out onto the water, pushing our whole weight with shovels, and absolutely trivial to return. You just can't push rope!