Fidelity Research FR64s Headshell dilemma


Dear FR64S users can you help me please. I have an FR64S that i bought without a headshell. I have only just got round to getting it mounted. I did pivot to spindle distance of 231.5 (the alternative distance' I also have an armboard for 230.
I tried a Sony headshell that i had - it was 2mm short of correct alignment. So I bought a new Jelco headshell it was also too short. 
CAn you tell me what headshell does work to allow other cartridges to work. I'm just using a DL103 for alignment first as I fettle the rest of my front end.

thanks
lohanimal
Dear chakster, your ''theory'' imply that one can chose spindle
to pivot distance as one like. But pivot to spindle distance determine
eff. length. By Stevenson 245 mm by Bearwald 246 mm. If one 
could chose eff. length as one please we would not need tangential
arms because all points on the record would have zero angular error.
Your Feickert can't correct all the errors manufacturer made. 
As I mentioned by Kessler&Pisha all 22 inspected tonearms have errors. 
By Stevenson 245 mm by Bearwald 246 mm

This is why a cartridge must be moved just a little bit forward in the headshell and a little bit turned to the side to align by cantilever using lines on the protractor.

As i said earlier there are many turntables with fixed tonearms, you can’t change PS distance, but you can change alignment method moving a cartridge only (in the headshell slots).
BTW there are 9'', 10'' and 12'' tonearms. My Kuzma is made
for 9'' while my SP-10 does not allow 9'' tonearm. For tonearms
with different length different spindle to pivot distance are
needed. Ergo: one can't  chose this distance as one please. 
If we do speak about scientific arguments we have to use science principles.
I can see hypothesis - geometry. A lot of very exact calculations from derived data. Although I was thought in the university that after hypothesis you have to do experiment which must be reproducible. I do see a lot of calculations. What I don't see actual measurement with test disc using dedicated setup like old days system produced by Bruel & kjaer. So I think that Japanese geometry is problem related to that we can speak a lot, make a lot figures that manufacturers are stupid. Although at the very end measurement is the easiest way to decide.
Dear chakster, the so called ''zero points'' on the record will be
on other ''points'' by Bearwald than Stevenson. That is the
whole point. Those points determine  the amount of the angle
errors made by each geometry. You may have eff. length right
but if your PS is different you obviously negate their mutual
dependance. Aka PS+ overhang= eff. length .

 .