Welcome, AZSkibo - I've got two E M Reilly double rifles in .500BPE. The first has serial # 18766 and the second #18954. Like yours, mine are extensively engraved and in wonderful condition, bores and all. The earlier one has Damascus barrels and the latter rust blue. I'd be interested in learning the composition of your barrels.
According to the only reference I've been able to find, Volume 3 of Nigel Brown's BRITISH GUNMAKERS, it appears you're in the same vague situation I am. That is, your Reilly as well as my two are listed as being made sometime between the years 1868 and 1875.
The first serial number listed in this range is 16,273 with the last being 20,827.
Both of my rifles have the same London and Paris addresses on the barrels. I'm interested in your source regarding the closing of the Paris "storefront" closing in 1872. Brown makes the following statement; "There was a Paris branch in the Rue Scribe certainly in the 1870s and 1880s."
The title of your first post is "YET ANOTHER Reilly (.500 BPE). This leads me to believe that you perhaps have another Reilly if not more. Is this so? I'd be very interested in hearing about any other you may own.
Best Regards - Marc (Krakow Kid)
