However, I'm still too stuck on the "not from the heart, but from another part" phrasing - as surely worrying about Fredersdorf being threateningly ill would have been very much a matter of the heart to Fritz

Okay! A native speaker friend of a friend has weighed in, and her interpretation is that Fritz is saying that, although he feels the pain from the bottom of his heart, it's not his heart *qua biological organ* that's causing the pain, but his mind that's causing his (metaphorical) heart emotional distress.

Which is absolutely consistent with the rest of the letter and makes perfect sense to me. And which does not help us distinguish between Groeben and Fredersdorf. ;)