I agree with late 1880 and before 1891. But i have still the problem in the time frame with the cartridge .22 long.
The earliest notice i know for making the .22 long in germany is from 1899, RWS Stadeln made the .22 long with blackpowder at this time.
The question is- when it is chambered in origin for the .22 long- if Dreyse would have build an rifle for imported ammo.
But it is interesting that Dreyse used obviously running serial numbers.