Holy buckets!
I've never seen one in that far. About the only advice I would have is to use water to free it. Yeah, it sounds counter-intuitive, but wait until there's a relatively warm day (thinking next weekend here) where air temps are in the upper 20s or 30s. Take a generator and a couple of sump pumps with garden hoses. Drill a couple holes for putting the sump pumps down into the lake and use the "warm" water of the lake (try taking water from several feet below the ice) and use it to melt the ice holding the shack down. This WILL take some time!
Running water will eat away at the ice and if you do it on a day where the air temps are high enough you should be able to free the frame and sides of the Ice Castle. You will also probably want to drill a couple holes nearby to let the excess water you are pumping up onto the lake surface to drain back below the ice.
This would be a hell of a mess, but it is the only thing I can think of at this point. I am guessing that on a "nice" day, this will take 4-8 hours of work to free it up. As for the initial tow, I would suggest a vehicle with a winch sitting at a decent distance maintaining a steady bind on the hitch/frame to where once it comes loose you will see it move.
Note, as you have already noticed, chiseling a sunken ice house out when water is able to find a way to come up through cracks/hole in the ice is a losing proposition at these temps and your current situation.
I'd be very interested in how this all works out for you and your bud!
Note, ignore the ice inside the shack except for where it is holding the castle down like around the holes. Actually, I think I'd drill the holes out and let them serve as the drains! And remember, you will be working in 18" of standing water by the sounds of it. The trick here is to just let moving water do the work for you.