I do not live in a climate where this is an issue but perhaps my idea
can help.
Construct a floating device that has a measuring device consisting of a
horizontal oriented probe that contacts the underside of the ice when
pulled up by a motor with a measuring module attached to it. The way it
would operate is to deploy it with the probe extended past the maximum
expected ice thickness. To take a measurement the rod attached to the
probe is heated to free it from any ice and it is then retracted until
it reaches a stopping point on the underside of the ice. The thickness
can thus be determined. Subsequently the probe is extended and the
heater turned off until the next measurement.
Of course this is a concept and I have not determined how to make it
robust or how to deal with fouling or unknown problems.
Dan