Can you help me find the right stem (or knob) for this 20-year old Symmons
Temptrol shower faucet?

My Symmons Model=CA faucet stem broach splines are the wrong size!

Details:
* The shower faucet has a circular brass plate stamped "Symmons" "Model CA"
* Naturally I assumed it's a Symmons faucet so I called them for parts
* Symmons kindly sent beautifully machined parts; (almost) all fit nicely:
- The TA-10 Temptrol "spindle assembly" is a gorgeous work of art
- The TA-25B "black diverter spindle kit" was a 100% perfect replacement
- The TA-4 Temptrol "hot and cold seat kit" was likewise elegantly machined
- The TA-35A "cold seat removal tool" fit the larger cold seat perfectly
- The TA-35B "hot seat removal tool" likewise nicely fit the smaller seat
- Even the installation diagram & instructions were perfectly aligned with
what I have in my 20-year old shower faucet
http://common.csnstores.com/common/m...s/sym1010b.pdf

The only problem is the faucet stem broach splines are the wrong size:
* The Symmons spline is circular, 12 point, ~0.415 inches in diameter
* My brass spline is circular, 16 point, ~0.360 inches in diameter

Have you run into this problem before?
How do you solve it?