Avid, welcome to Nitro Express Forums!

A few thoughts:
1) Straight case? It could be an 11.6x65R OR an 11.6x63R
http://www.cartridgecollector.net/tags/european-sporting-11mm-upwards?page=2
Best to slug the bore and check the twist rate as well because the "11.5" (.4527") may well be the proof mark that would have been "bore" diameter NOT "groove" diameter and not what calibre ammunition.
You may already know this, but plenty of the old black powder rifles/ammunition used somewhat undersized bullets that "bumped up" to the grooves with black powder. A purely groove diameter bullet may not fit in the case.

2) 65mm is 2.56" so "if" the case head and rim thickness is the correct size you don't need to obsess about .450 NE "thick rim" brass. Just find .450/.400 3" Jeffery, it's the "thick rim" and you can trim it to length. You still need to be very sure of the depth of the actual rim seat on the rifle tho. May require thinning the .450 "thick rim" (~.065") a bit.

3) Be very careful of your interpretation of "….powder slower than 2400 and work from 40% of the black powder charge…."
Not so simple. That 40% really ONLY applies to H4198. Yes, other powders can work but likely not at a simple % ratio. Plus you "may" have to use a case filler like dacron or foam backer rod and magnum primers to achieve reliable ignition.

4) I'd suggest that your gunsmith can probably look at the rifle and give his blessing that it is safe to shoot…..but…..that does not mean that said gunsmith is familiar enough with loading and shooting antique black powder rifles to blindly accept any further advise as to loading practice with "Nitro for Black".

There is a fair amount of published material to do with smokeless in black powder cartridges, I'd suggest searching them out and getting familiar with the issues before proceeding.
As this is a double rifle you may be limited in choice of bullet weights, grease groove, paper patch, etc.
If a ~.45 caliber I would opine that it "likely" will only regulate with somewhat lighter bullets, on the order of 300 maybe up to 350 grains.
I'd start with 325 to 350 grain bullets sized to groove diameter for any smokeless load.

Stick solely to cast bullets…..

- Mike