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
bukanona, the problem of the inner grove distortions is not invented
by hypothesis. The problem can be easy solved by reduction of
playing time on each side of the record. That is to say to avoid
critical part of the inner grove. People don't buy records depending
from time duration. This also means no need for Stevenson geometry.
Nandric, show me measurements not geometry assumptions.
I don't neglect models.
I am not believer in Stevenson or Baerwald superiority. 
bukanona, What do you want to measure, tracking angle error or the distortion that results?  The former is completely predictable using geometry handed to us by the Greeks and their mathematical descendants.  The latter is complex, because you would need a test LP that encoded a single test tone, e.g., 1 kHz, from outer to inner grooves.  It would be useful to have such a test LP, but I don't think it exists.
@karl_desch 
You have read, experienced and understood the same problem. The only thing you mis-understood was that i had thought 230mm only allows stevenson.
I was perhaps under the mis-apprehension that 230mm ONLY allows stevenson.
@rauliruegas I appeciate you sending me the link repeatedly - but my question related to cartridge shell alignment using Lofgren A at 231.5 - not what the actual distortion figures are. However, it, is nevertheless particularly useful as it shows and confirms what @dover has said and pointed out - namely that at 230mm one can do Bearwald, Lofgren etc.
Likewise @dover having experiences the same head-shell length thing confirms i am not going insane - i ought to try a cartridge that is longer or has a longer cantilever to try out 231.5 or get a longer head-shell. Until then I will use 230mm
For my purposes thanks and thanks again for the advice.
Yes lewm measurement is a key. In the modelling then geometry was used to measure land in ancient Egypt results was easier predictable. Tonearm is much more complex.
To order such LP with 1 kHz tone is not big problem these days and even it's not expensive. Just someone has to make  methodology and try it for the sake of humanity :) After measurements we can discuss if 1 kHz tone is the right one but it will be figures not modelling.