I am curious to know who might have appraised this as being from 1820-1840? If by the previous owner, dealer-seller or paid appraiser, I can see that possibility but the Basses I have seen from German pre-1860 seem to have much more 'experience' evident.
Do you know if those tuners are original to that Scroll? If so, is that Scroll original to that Bass? If not, one or both do you know if the tuners were used from another Bass and put on that Bass?
I say this about the tuners because most basses I have seen with anything similar were estimated to date from 1880-1920. A big range in years but these Basses are mostly unlabelled so we usually hear of these 'ages' from dealers selling them. In my mind, that's not always the most reliable $ource of information.
On the Gears, I have seen some Gears like this pic below on several Basses from both Germany and England. I have a set myself that were on my Mystery English Bass. They date about 1820-1850 or so and are not the original to my bass as there were 4 of these. However, one of them was slightly different by about 5% at most, same handle and Gear but the teeth and handle engraving looked to be from a different batch so they could be original and a 4th added later. In this picture, you see 2 different Worms, same handles. Mine and the others I have seen had smaller Gears and shorter worms like the upper gear in the pic;
The style of your Bass, size, construction, Varnish etc. all suggest to my eye a later period closer to the 20th century. There were many makers in operation then making Basses that precede the commercial Wilfers, Pfretschner labelled Basses etc.. Karl Herrmann who branded his works 'Morelli' in the early 20th century was trained by one of the Dölling family. I have seen a few Dölling Basses pictured and they have a similar quality and patina as your Bass.