never tried a kh3, but things you can tweek for taming highs:
1). what tubes? if it has EH 12ax7's (bright tubes) take those out and install some JJ 12ax7s
2). Install a 250pf - 500pf cap in the tube riser board c1t or c2t spot
3). of course c3. I tend to like 0.0022uf there. CrunchBunch mentioned c3, I think he made a typo when he suggested 0.022 and 0.047uf. this would be way too large there, I think he meant 0.0022 or 0.0047
4). c8, and c9, use 0.022uf
5). use mallory (CDE) 150's in c3, c8, c9, and perhaps c17, and c16. These are warmer sounding caps.