But as Bruno said, all it takes is one period image to put this to rest.
It seems that 99.9% of the WW1 period photographs of Jäger zu Pferde and Kürassier show the soldier with his helmet covered by an Uberzug, making it virtually impossible to identify fittings.
I have only been able to uncover one period photograph that appears to show an uncovered JzP helmet.
The helmet has a leather chinstrap with the proper fittings and, though not strikingly clear, appears to show a smaller Kokarde.
The soldier is outfitted with, what appears to be, a KAR98a; also true to the period.
This photograph is copyrighted and the owner has disabled the download function, so I cannot post it here.
I can; however, provide a link that will enable the zoom feature. When zoomed into the helmet the outline of the Kokarde can be seen.
Though likely not conclusive proof, the photograph does provide compelling evidence:
https://www.flickr.com/photos/paranoid_womb/7204421390
Here is a photograph of my helmet:
This helmet shows very little wear. It may have never actually been issued.
John