WOW! From McMaster (NOT the cheapest source, but an easy place to find and price things quickly) here's a price:
1" diameter Vespel rods = $110 P E R I N C H ! !
YIPES!!

I would agree that using custom router bits and running lengths is the way to go.

You'll need to build a fixture that will hold the rods by the ends and is flippable, so you can run side A, then flip it and run side B.

Then, to shape the top (the 'third' side) you'd need another custom router bit and another fixture.

This fixture should be a groove that has been filled with silicone casting compound and the rod (with the first two cuts done, is set into the groove and vacuumed into place so you can accurately index that last router pass.

I have no idea how vespel machines or how harsh it is on tooling, but you may be able to have a local tool grinding shop do the custom tools for you, sicen the epth of cut will be less than 1/2" you can probably use a standard bit that has been modified.

Uh..... more thoughts...

If you cut accurate slots in each end of the rod, you could build a fixture that would pinch it end-to end (maybe 4" lengths at a time, for stiffness) and the router bit could do a complete side at a pass (including the top). Then flip the stock end-for-end, aligning it using those slots, and do the other side.

I would suggest a shaper cutter, since the depth of the cut would end up being half the width of the finished pick and a router bit would be problematic at that diameter.