The recommended brace height for this bow is 7 1/2 - 8". At 8", I was getting the clank sound I described. I raised it up to 8 1/4" and it was more of a poink sound, an improvement. At 8 1/2", the poink sound went away and all that was left was the string noise, about the same as the recurve limbs are making at an 8" brace height. This is with over twisting the stock string. Tomorrow, I will make a new string and see if I can reduce the sound even further, and maybe back off on the brace height a little. I'm happy with the sound at 8 1/2", but I don't know what that's doing to the arrow velocity. I'll run some tests with my chrono and see what the effect is on arrow speed.
Thanks for all your help, gentlemen! I'll probably try some of your other suggestions to see if I can reduce the sound even further.
This experience has been contrary to my expectations. I would have believed that a longbow would be inherently quieter than a recurve, and would be braced lower. For this particular bow, that doesn't seem to be the case.