I thought about cutting a hole like you said ,but have 2 problems.
The largest hole we are aloud to CUT in Ohio is 12" for ice fishing. ( talked to the DNR about this and about breaking thin ice to place decoys (1" or so ) and they look at any hole cut in ice that is safe to walk is a fishing hole and thin ice is just that thin ice)

The other is with all the snowmobiles out on the ice and people walking out to fish or hunt .
If some one snowmobiled or walked into the hole and drowned or was hurt the person cutting the hole would be liable ,both to get sued and arrested for neglance or homicide.

So IMO cutting a large hole like you say is a REAL BAD IDEA !!!!!