Personally I would rather get rid of those ATs, but if they are retained I think they should be addressed directly. E.g. the equipment table and armor description should say this is a heavy, encumbering long coat that is worn for protection against the elements, with little or no protective value. The current implication is that it is armor, and functionally that's just not true.
If you are going to have the system represent a heavy, encumbering long coat, I also think that it should actually have some protective value, or that it should not require Maneuvering In Armor skill.
A much better way to address this in my opinion is to decouple Quickness penalties from the weapon tables entirely, rather than trying to integrate the idea of mobility into both the table and also the DB. Then it's easy to say "this item will slow you down by this much". And "this item provides this much protection." It also handles more complicated situations, e.g. you are wearing a heavy coat (because of weather conditions) over chain mail (because you actually need some protection). Just increase the Qu penalty, and use the best applicable AT.