Is a HEPA furnace filter a good option?

Unfortunately, probably not. A HEPA filter works extremely well—it traps most of the particles that pass through it, even particles as small as .3 microns. But to capture such minute particles, it uses very dense filtration materials. And it's much harder for air to pass through these materials.

Standard home HVAC systems simply cannot generate the air pressure that is required to “suck” air through a dense HEPA filter. In fact, to use a HEPA filter, you must install a separate HEPA filtration system that “boosts” a certain portion of the air flow through your furnace to generate the required air pressure.