Despite the similar naming scheme, the 3HC* is actually GR rather than a Haefner piece. It does not have the Haefner blank, but a GR blank. It's either the standard or symphonic blank - I can't remember which one for certain but I think it was the classic blank. (When I tried out some of the C* and C** mouthpieces one had the symphonic blank, and I seem to remember it was the C**.) You'd have to email the GR folks to find out for sure.
The symphonic blank is similar to the Haefner, just a little heavier because it doesn't have the grooves that the Haefner blank has. The classic blank differs more. Rather than me trying to describe the difference and doing a lousy job, I'll refer you to the
pictures on the GR web site.
Sorry not to have a complete answer, but hope this helps some.