I'll add that IMO replacing an extension cord with a solar + battery intallation doesn't really meaningfully negate risk of fire. The risk of fire is caused by having electricity in or on the coop. Whether it arrives from the grid or from a battery is in effect irrelevant.
There's no way a solar and battery solution for 80 watts costs $2,500. This should be operable under a 200w panel (~$200), 30A charge controller ($150), and a 100AH deep cycle marine battery ($370), add another $50 for miscellaneous connectors, wire and accessories. We're looking at well under...
Keep in mind the de-icer that the OP linked is a thermostatically controlled unit that will not produce a constant draw. I have connected my de-icer to a kill-o-watt meter during a cold stretch where it was constantly below freezing here in Ohio last winter. Unfortunately I don't recall the...