Multicoating on the outside may not be necessary. The outermost element, if it reflects, will simply reflect light out and away from the camera. That won't actually cause any problems for your photos, since the light never enters the lens and therefor never reaches the sensor.
A coating on the inside of the filter is more important, as it is the internal reflection that bounce around off of the various lens emenents and even the back of a filter that can create ghosting. Ghosting is that telescopic set of usually aperture-shaped reflections that occur when a bright nearly-off-axis light source (i.e. the sun in the corner of your image) causes those reflections to occur.
By multicoating the inside of the filter, Hoya is able to cancel out a lot of any potential ghosts that reach it. The inner coating is much more important than the outer coating. Having an outer coating as well may help reduce flare and maintain higher contrast, as it could potentially allow light to pass through the filter and into the lens without the same kind of losses as without a coating (an uncoated glass element is going to reflect more than a coated glass element), but I think those problems would be more subtle than ghosting, which is very likely the "failure" you are seeing.
If you are indeed seeing ghosting, it don't think switching to a filter that is coated on both sides is going to really change anything. With a powerful enough light source, multicoated lenses are still going to flare and ghost. The sun can pretty much cause both in pretty much any lens. The only way to significantly reduce ghosting and flare from such powerful light sources is to use lenses that nanocoat (rather than multicoat) the most critical internal elements that usually cause the most egregious problems.