Just interested in seeing the wacky boar's head from the base of your bottle, sorry if I missed it. There are at least 8-12 versions of the boar that I’ve seen. Here is my GOrdon's collection, the aqua one is similar in age to yours it looks like. Lots of bubbles and uneven glass. I Also have three post prohibition "linden nj" versions, 2 pints and a fifth. The fifth is from 1949 so they were still using the boars head at that later date.
Best guess on my aqua bottle is 1905-1920. There is an aqua one from about the same time, more like 1895-1910 that has London England embossed on front. Glad there were so many gin drinkers!
Your boar's head shape is quite close to mine. Best guess would be 1910-1920 when prohibition kicked in. It's possible it is earlier than 1910 by a bit, but there isn't any definitive way to know, and the crudeness of the glass (bubbles, thickness diffs etc) are a sign of a bottle that is in the earlier part of that range, but by no means conclusive. Here is a pic from Etsy of that earlier version that I spoke of with the vertical Gordons, and London England embossed. That version is in the 1895-1910 range and worth a few more $$. The registered number you mention has more to do with Gordons Distillers registration than any bottle ID. That same 610617 number is on many Gordons bottles from different eras.