When no one else steps up there's only one way, so I read the Laundry series and the Irish story myself, paying attention to any references to Erich Zann. These are my findings.
The Laundry Series by Charles Stross
This series of books feature a violin designed by Erich Zann.
1. The Atrocity Archives
No mention of either violin or Erich Zann.
2. The Jennifer Morgue
The violin is mentioned and described as an Erich Zann model, but no details are given.
3. The Fuller Memorandum
The history and origin of the violin is briefly sketched, but there's nothing new about Erich Zann himself.
Chapter 6, "Red Orchestra", last section
He's read about its like before. Their design is attributed to a deaf-mute German violinist in Paris in the early 1920s, but nobody actually built one until the ghastly Dr. Mabuse commisssioned an entire string section from a certain Berlin instrument maker in 1931. (It should be no surprise that the instrument maker prospered under the subsequent regime, but was excecuted after a summary trial by SMERSH investigators in 1946.) This particular instrument made its way to the West in the luggage of a returning GI, was retrofitted with electric pickups during the 1950s, and after a spectacular run of accidents was acquired by a reclusive collector in 1962 -- believed by some to be a front for a British government department who, as a matter of state policy, did not like to see such instruments in the wrong hands.
It's not entirely clear who this "certain Berlin instrument maker in 1931" is, since Lovecraft's original story implies that Erich Zann died in the early 20s (at least the narrator was convinced of this), but book #6 (The Annihilation Score) makes it clear that it is indeed Erich Zann being referenced here.
Here, then, Zann is associated with Berlin.
Interestingly, I don't believe Erich Zann was described as deaf in Lovecraft's story, only mute. If I recall, he could hear the narrator just fine but had to write his replies.
4. The Apocalypse Codex
The violin is mentioned and described as an Erich Zann, but no new details.
5. The Rhesus Chart
The violin is mentioned and described as an Erich Zann. Mo gives it the name "Lecter", which seems to be her personal name for it, not its "true" name. No details about Erich Zann.
6. The Annihilation Score
The violin features prominently. A little more is learned of its origin, though not that much about Erich Zann himself. Still, it's the most details we get, at least until more books are written in the series.
Chapter 2, "Morning After", p. 19 in my edition
He means the orchestra of his victims, the musicians he has twisted and killed over the decades since his grisly genesis in Erich Zann's workshop in 1931. He was created at the behest of one Professor [sic] Doktor Mabuse. Mabuse the Gambler was a monster, and Zann his enabler—but Lecter has outlasted and surpassed both of them.
Chapter 15, "Fresh Meat", p. 294 in my edition
Your sidekick Mr. Grenade stops being your friend the moment you pull his pin out: just so with the violins Erich Zann created at the behest of Dr. Mabuse.
Chapter 19, "The King in Yellow", p. 378 in my edition
[...] The King in Yellow was converted to an opera but never performed in full; Franz Kafka prepared the libretto and a score was subsequently written by his collaborator, the violinist Erich Zann, for performance on specially adapted instruments of his own devising, but the rise of fascism put an end to all attempts to perform it until after the war. [...]
"Until now, that is. With the recovery of the original score we are delighted to present, for the first time, the extraordinary violin sonata from the second act that marked the zenith of Erich Zann's career. [...]
p. 380 in my edition
The violin in my hands feels alive by proxy. As the piece moves back to the major theme, I feel him, warm and pulsing with stolen life, all the lives he's drunk down over the years and decades since the mad luthier of Munich bound a summoned demon into an instrument carved from the still-raw bones of human sacrifices: [...]
So in Stross' universe, Erich Zann didn't die at the end of Lovecraft's story, but lived into the thirties and forties where he fashioned the white violins for Dr. Mabuse.
Stross also associates Erich Zann with Munich here (in The Fuller Memorandum it was Berlin), whereas The Silence of Erica Zann implies that he came from Stuttgart (at least by the time he moved to Paris).
Kafka died in 1924, at least in the real world.
7. The Nightmare Stacks
No mention of either violin or Erich Zann.
8. The Delirium Brief
The violin is mentioned a few times, but no details, and no mention of Erich Zann.
Paappana, or Erkki Santanen's Music
I can't read the original Irish, but I managed to find an English edition of the book (The Book of Poison) from 2014, translated by Colin Parmar.
Aside from the theme, and the possible allusion in the name Erkki Santanen, this story seems to have nothing to do with Erich Zann or his instruments. There are no references in it to Lovecraft's story.
It was first published (in Irish) in 2010, and the story appears to take place in modern times (in Finland, curiously enough given its original language.) It could be that Erkki Santanen, like Erika Zann, is somehow related to Erich Zann, but there's really nothing in there to support such speculation.
If we take Stross' books as part of canon, Erich Zann (or at least something masquerading as Erich Zann) survived into the thirties and forties in order to create his violins for Dr. Mabuse. This actually matches with the letters dated 1924-25 in Silence, so I'm going to accept it as true.
Either way, the Laundry series and Paappana give us no new insight into Erich Zann's life before the events of Music or of his family, meaning the timeline from my original question and M. A. Golding's answer is likely the closest we can come, as I am not aware of any other potential sources.
This is my own revised timeline:
- 1870 or earlier: Erich Zann is born.
- 1910s: Erich Zann has one or more children, at least one of which is a son. Being most likely no younger than 40, it may not be his first marriage.
- 1920-22: Erich Zann leaves his family, then living in Stuttgart, and moves to Paris. Here the events of Music take place and he is presumed dead by the narrator. Erich, or something masquerading as Erich, does indeed survive.
- 1924-5: Still in Paris, Erich sends letters to his family, then becomes incommunicado. Police in Paris declare him missing.
- 1931: Erich Zann, possibly now living in Munich, creates his infamous violins for Dr. Mabuse. He may relocate to Berlin, it's not entirely clear.
- 1946: Erich Zann is supposedly executed.
- 1945-1947: Erich Zann's son, probably 30-35 years old, has a daughter: Erika Zann. She may have siblings, we can't say. The family seeks refuge post-war in the USA.
- 1976: Events of Silence. Erika Zann, around 30 years old, perishes. She likely leaves no children of her own.