For a fish bellied rod like that the two tapered ends will only be 2" long, I would just set the topslide at a slight angle. Basically diveid ethe length into three, leave the middle at 5/16 and taper the two ends from 5/16 down to 1/4" and then blend the transition with a file.
All these were done that way.

Take a look at the first few photos in this album of mine, to see the principal
Better still part way down this page is the post I used the images for with an explanation
J
PS don't try Neils suggestion as that won't work for the tapers you require the tailstock woul need to be set over atleast 3/32" not 1/32"
Edited By JasonB on 09/08/2015 16:07:54