I'm also very suspicious of the pIqad scripts, which look like something created by a graphic designer who never had to actually write the language down. The graphemes for <q> and <Q> in particular look awfully similar.
However, the banner for Qo'noS QonoS, looks really good in a blackletter face. Perhaps Klingon just has a font problem: isn't this better, in Unifraktur Cook?
It may be as affected as the heavy-metal umlaut, but I think there's more to it. Klingon uses both capital and lower-case H, although the latter is only used in the digraphs
Libre blackletter fonts are not in great supply; Dieter Steffman made some gratis ones, but for Web typography the likeliest choice is the Unifraktur faces, available in Google Web Fonts.