The 50-110 case is going to be a bit large at the case head, and the rims likely a bit thin, so it would take some pretty serious swaging equipment. Buffalo Arms sometimes when they can get the 50-110 or 348 cases reforms them.
I have on occasion trimmed 45 2.4 cases down to 2,275, size them in the 44 die,fire formed them and trimmed to length for 44-77, letting the case headspace on the shoulder instead of the rim. They do get a small swell at the web but at the pressures bp runs at it hasn't been a problem. So it may be an option for you to simply run some 2.6 cases in your 44 size die , fire form and trim.

2.4 cases will come up a bit short,for the bottleneck, but if you’re wanting a 44 rifle, the 442,4 st is a really good one. Then all you need is a set of dies to go with your cases and a godd 448 grease groove mould or a a 43x papep patch mold

Appreciate the information.  I have some 60  .348 cases however they are really expensive through Starline.  Has anyone tried 50-110?  A little more affordable.  I already have the BN dies but a straight case would have been preferable.

There is always the Remington .44-90 necked. They can be made using .45 brass. I think they used a 505" or .506" base diameter.
That would be a lot easier to come up with brass if your wanting to shoot a .44 bottlenecked shell.
A couple friends just got a .44-90 bn Sharps and I gave them 150 cases to get them shooting them. 
I have two .44-90 bn Sharps and it is a fine caliber as well as the .44-77's I shoot.
You might do a search for some .44 Bell basic, Huntington or Jamison brass, there might still be some floating around.
But your 2-7/16 might be a .44 run special necked.

I just looked up the .44-90 Rem special Necked. The base diameter was .506"
Rim diameter .628"
case length 2.44"
Shoulder diameter .504"
If this is your chamber the .45-2.6 brass will work.
Kurt