Please have a look here:
The clip shows two versions that could be your solution. There is also shortly a switch in the “Generator>Type” but I assume, that looks not as you would like to have it.The size would be adjusted within the Material “Thickness” then.
To make it work as you like, the alternative could be an copy of the Hair Object, as the “Rachis (Shaft)” [or bone] doesn’t show. As second option one could take the Hair Object away from the Feather set up, and while active, call up an Instance Object and place this new Instance underneath the Feather. In both ways the Hair Material for the Rachis will work as shown in the little clip. I assume that the visual part are the key, so please compare the results. The options in the Render Settings have changed since and R18 doesn’t have some of the options anymore. See image:
If you have any doubts, please ask the Render service for a test render, or check with the Support:
About the “regular” set up: a Sweep based set up is suggested:
Please check out bullet point #5
I hope that helps a little bit to get what you need for your project
My best wishes