At first I couldn't believe you had it braced that high, but then I re-read and noticed that you are measureing from the back of the bow rather than the belly side, so that makes sense. I have my selfbows braced about 5 to 5.5, but from the belly side, so that figures to roughly the same thing measuring to the back.
You could try a few things: 1) go ahead and raise the brace a little bit if it seems to be performing okay. 2) strip your fletching off and back it up a little if there is room to do so without it hitting your fingers on the release. 3) strip you fletching off and use shorter feathers. Might have to go from a 3 fletch to a 4 or a 2 to a 3 in that case to get good flight. If you are trying for some serious historical or period accuracy and replication, then that's obviously a no-go. But if you are just trying to get arrows to perform well, then it's an option. I've done that with a couple. And 4) any combination of the above. Raise the brace a turn or three; use more, shorter feathers; and back the up a little.
Enjoy playing with it!! This is the fun stuff. Let us know how it turns out, espically if you raise the brace much.