Low-pass filter for high power application
Directly filtering AC mains is a design decision typically used only on the grid itself, where reactors can be the size of  cars and need no special considerations for cooling and will last for 50 years. Even then, that is typically a technique for reactive grounding.

You already said that you are probably going to modify the heater, so let's look at the overall problem. At this point in the design process, we have to solicit all alternatives and make choices based on effectiveness and economics. Depending on scale and severity of the problem, you have to consider the cost of a big mains filter versus the cost of other techniques. Bear in mind that that big filter is going to need cooling, either directly or by a potentially more expensive air conditioning bill. Its not very likely, but the expenses might balance out in favor of the added benefit of a double converting UPS. Large installations do this too, but when they get really large a motor generator with an attached diesel engine (commonly called a diesel UPS) may be a better option.