Here's an idea....they make Additional Versions of said headgear so that it fits the Beastrace.
I know, tall order....but if they made the races, they should make accommodating headgear. Other games do it, FFXIV should do it to.
Or, an idea I proposed several times before in our Hrothgar threads, they could make LV1 gear of many different fashions and ideas from Hats, Helms, and otherwise, to make up for it.
Make them dyable, and easily available at Starting Gear Vendors. Like where you would buy the ability to get claws.
(But honestly they need to delete that, and just put it into the CC, like for real.)