Sounds like a good idea, but the glass would need to be fairly thick I'd think, and perhaps too heavy for the application, causing imbalance? Thin steel shaped might be better?
Although I realise you could move the hanging point to compensate.......perhaps @chunkolini would want to do that for fear of spoiling the aesthetic appeal?
I will try and keep the shape free of additions, I reckon upswept wingtips and a dihedral angle might do it. I'll start there first.
It may even self register as it is.
How about a perspex "vane" fitted inside the body to help keep the head into the wind, simple trial as can be retrofitted,removed ,as usual chunks excellent stuff
Chris