I actually live in Dawson and am quite familiar with the bottles produced here. I have never seen another like it and since most of the town was industrialized over the exact spots of some of the bottlers I would say that there are none in existence. Sorry.
I still have not come across anything for you. I have done more research and cannot find where the bottler was located. The Sanborn FI Maps do little to help since they mainly show the square around the courthouse. I am afraid that unless someone has this in a private collection, there are either none in existence or your best bet would be to dig privys in Dawson. Did you find the shard in Dawson?
you have the bottom half of a coffin whiskey this is a very thin walled bottle they are hard to find , there are a lot more coffin whiskeys out there in many small cities , minneapolis has over 200 hundred different coffin whiskeys . your bottle whole would look like this
if you want that bottle you will have to get in some privies in town , get into enough of them and you will find it , also privies are not as hard on the bottles as dumps are , having dug around 170 privies last year with my digging partners we found a total of about 10 embossed whiskies , in georgia i am sure a person could dig year around , in minnesota digging is over till april for the most part