Playing like everyone else wasn't difficult enough for Fripp, so he invented New Standard Tuning
https://en.m.wikipedia.org/wiki/New_standard_tuning The guitar's strings are assigned the notes C2-G2-D3-A3-E4-G4 (from lowest to highest); the five lowest open strings are each tuned to an interval of a perfect fifth {(C,G),(G,D),(D,A),(A,E)}; the two highest strings are a minor third apart (E,G).
It presents particular issues for bass;
http://www.talkbass.com/threads/fripp-tuning.914734/ My favorite comment:
Use the thickest taper-core low B you can find. I use a Sadowsky black label flat at 0.130T for this tuning (and while it's cool you call it Fripp tuning, violincellos have been tuned like this for over 300 years, so let's not give Fripp credit for everything!).
TI jazz flats have a 0.136, but it's not a taper-core if I recall correctly. The taper core will seat the string lower in the saddle and hopefully will solve your problem (you're still a bit sharp, correct?).
I'll try it, as soon as I get the hang of (B)EADG tuning. It should only take another lifetime or two. Let me know how it works out for you.