OK, it's not a double rifle but it is Belgian and not German/Austrian and it was made for the US market so here it is. In the 1890s H. Pieper of Belgium made some Cape guns in 12 gauge and US rifle calibers for the US that were marketed by Montgomery Ward and Sears Roebuck. The rifle calibers Sears offered were 38-55, 44-40, and 32-20. I've read that Montgomery Ward's 1893 catalog listed a 40-60 (I've ordered a reprint to check this out). I've seen a post someone made that he had one in 30-30 but I would need to see that offering in print. They were back action hammer doubles in both top lever and side lever models and utilized what today would be called mono-block construction. I have had one for some time that was marketed as a 38-40 although no caliber is marked. The groove diameter is slightly over sized for the 38-40 at .406 vs .402. I chalked that up to manufacturing tolerance or something and have been shooting it with .406 diameter cast bullets as a 38-40. It is quite accurate. The chamber is a little sloppy in the neck (tolerance or something again?) so I was playing with it the other day and just happened to drop a 44-40 round in the chamber. It went right in. On general principles I'm not going to shoot a .427 bullet into a .406 barrel. Can it be possible that this is what was going on with the "44-40" guns? The rifle barrel is quite sturdy and it may have worked. Does anyone have one of these in "44-40" and has slugged the barrel? Later ones were marked 44-40 on the rifle barrel. To make it interesting, Pieper also made some single shot rifles on Martini actions in 44-40 that may have been marketed to Australia as kangaroo rifles!

HalfaDouble.
You likely have a 38-40 chambered rifle that was made using the closest size barrel they had in stock. At this time, they paid more attention to "bore" diameter than groove diameter. They probably didn't have a large enough order to make manufacturing special barrel blanks worthwhile. If you can drop a .427" bullet into a case fired in your rifle, you could likely use 44-40 ammo, but since you are having good luck with your loads and have the "set up", it doesn't make much sense. The 38-40 is notorious( even in old American guns) for having oversize chambers. At one time I was loading for a modern Colt clone, an original mod 92 Win. and an orig. High Wall, all in 38-40( comparing different loads). I had to set the sizing die for each individual chamber to avoid ruining all my cases. By doing this though, I had satisfactory case life( I also seated bullets and crimped in different operations).
Mike

Years ago I had a Pieper 12ga shotgun that had a front trigger that was a set trigger. I assumed had been a two barrel set and the missing barrels were a cape gun setup with the rifle on the set trigger.

It had a Greener crossbolt, the guy I sold it to thought he was going to build a double rifle on it. I should have done that, the barrels were badly pitted, only thing it was good for.