There is no need to speculate about .600 NE.
The early breech loading hunting rifles used cartridges of various types (pinfire, Lancaster, Teschner, Dreyse, whatever more), brass or cardboard hulls of various length. 24 gauge was a common caliber, bullets were stubby things with a rounded head (in German "Katzenkopf-Geschoss), ballistics similar to, but possibly inferior to muzzleloaders. Used for hunting deer, wild boar etc in Germany, also Austria etc. Gravitation to the East??
All these constructs soon became obsolete with the development of BPE cartidges and then (for Germany) with the 11,15x60R in 1871.
And these again were obsolete by 1888.
These were expensive times for hunters - every 10 or 15 years your up-to-date equipment was thoroughly obsolete.

Nothing excentric about Teschner-Collath guns (except the locking principle). They were produced until WWII, chambered for nitro cartridges, and obviously plenty strong.

fuhrmann