50-90(110) sharps?

I had for a short time an MGM Encore barrel in 50-70 Gov. It was a carbine length barrel with light contour. For me it was too light and punishing even with moderate loads. The Encore with modern brass in 50-70 will handle pressures three times greater than the cartridge was originally intended for. With those type of loads a person would have to have sadistic tendencies to even consider shooting them. That said the 50-90 on the same platform is a magnum version of the shorter kin. The 50-70 case is 1.75" length and the 50-90 is 2.5"
If I were to try again with an Encore I would stay with the shorter case because if your shooting smokeless powder it has all the room you need. I would also go with a very heavy contour to add as much weight as possible.
I like shooting. For me its the most fun thing I can do with my clothes on. When shooting hurts its no longer fun.

In determining recoil energy part of the equation is total projectile weight. This will include the total weight of the bullet, powder charge, and any wad material that may be used.
A 90gn weight charge of black powder that may produce the same velocity as say a 17gn charge of Unique will have far more recoil because the total projectile weight is much higher with the BP load even though the actual bullet weight and velocity is the same.
With the 50-90 at 2.5" case length you could if the situation called for also use 50-70 at 1.75" case length ammo. With the 50-110 at 2.4" case length you can also use 50 AK at 2.2" case length. The rims are different so all will not safely interchange due to head space difference.

it does not look good....
en.wikipedia.org/wiki/.50-90_Sharps
en.wikipedia.org/wiki/.50-70_Government

Yes 50-70 Gov and 50-90 Sharps use the same rim so the same relationship exists as with the 44 mag/special.
Reading the link you provided it says the 5-90, 50-100, and 50-110 Sharps all use the same case with different charges of powder and bullet weight. This may be true but the 50-110 Winchester uses a different case that is shorter by .1" than the Sharps version with thinner and smaller diameter rim. This being the case the 50-110 Sharps and 50-110 Winchester are completely different cartridges. The 50-110 Winchester was an express loading for the model 1886 Winchester rifle. The express loading used a very light for caliber bullet pushed as fast as black powder could make it go.
I have an original mold for the 50-95 Winchester in the model 1876 rifle express loading and the same bullet was used for the 50-110 express loading in the Win model 1886. This mold cast in pure lead drops a bullet at about 300gn. With alloyed lead like enriched WW at about 280gn.
These express rifles used not only the light bullets but also used very slow twist rifling that would only stabilize these light for caliber bullets. Heavier longer bullets would just tumble from these barrels.
The 45-90 Winchester for the model 1886 rifle was another express loading that used a slower that standard twist. It would handle up to about a 350gn bullet. The rifles of these models that I have seen have been stamped with the word express with the caliber stamping. The express stamping designates the slow rifling twist rate.

The old stand by in the Lyman/Ideal 515141 has always been a good performer. It will run 425 to 450gn depending on the alloy used. It is a near copy of the original arsenal design for the 50-70 sans the hollow base. I once shot an elk with an original Sharps conversion carbine in 50-70. The load was 60gn of Goex FG with the 515141. Distance was maybe 35 yards for the shot. Shot angle was straight on and the bullet landed center of the chest and exited through the fertilizer vent. Velocity was about 1000 fps. Small bull just tipped over side ways and was done.
That bullet in air cooled WW or even softer down to pure lead will work fine at 1200 to 1400 fps. I sell a lot of conical bullets cast in pure lead to the ML guys and they do some good shooting to about 1500 fps.
I personally started shooting paper patch bullets in these type of cartridges for hunting and those are now my preference. I believe all the ammo produced by the Sharps company used paper patch bullets. We are certainly not short on designs in both lube groove and paper patch type in 50 caliber.

Good morning
For my all and anything plinker in the 50 Alaskan I am shooting a 410 grain flat nose plain base bullet. Mold is an LBT .512 400 LFN. From WW + 1 % tin this one drops at 411 grains. Have no doubt this bullet running at 1400 fps will go through any 250 pound plus white tail from any angle. Would make a fine "shoulder bullet".
Have not yet cast any of range scrap but will and try to get a yote to call into it. ILLinois does not yet trust us to blast corn crunchers with center fire rifles.
My other bullet I use in the 50 AK for now is a NEI .510 520 grain RNGC that drops at 525 when cast from WW + 25% Lino. This is the "Toyoto Stopper". Water dropped it hardens at .517. Two stage diameter reduction with a .515 then .512 die makes it much easier. Again cast from range scrap one day I would expect it to weigh near 540 grains and be deadly on any critter this side of our world north or south. At 1400 fps there is no elk, moose or foraging bear that would need to be feared.
With the single shots you have that capacity to seat the cast out long so powder capacity is not going to be a problem. In the 50 AK I have just so much space in the 86 Winchester to work with. So far is not an issue. But in a single shot I would use the slowest powder possible to get my velocity and smile a bunch at the reduced recoil pulse.

The more F's there are the higher the pressure will be for any given volume. For the load I mentioned using the original 50-70 Sharps carbine I was shooting the 515141 with 60gn FG actual weight not volume measurement and it shot through the elk length wise.

The f's are a reference to the size of the kernels of the powder. The more F's the smaller the kernels. The smaller the kernels the more actual weight there will be for a given volume. That is the reason I said the more F's the higher the pressure because more F's means more actual weight per given volume. Its kinda like filling a case with a large kernel extruded smokeless powder and filling the same case with fine ball powder. The ball powder of the same volume will weigh more because it more densely fills the case than the extruded powder.

You wont get any beatings here. Funny you make the comparison of the 500 S&W to the 50-70 gov. That is exactly the thought I had when they announced the cartridge. They could have just stayed with the 50-70 but then someone would have put the modern high pressure S&W version in an old Trap Door and BOOM!!!
There was also the legal angle with BATF classifying any rifled bore/groove over .500" diameter as a destructive device and so requiring special permits.
I think that any pre existing cartridges received a grandfather clause so are still with us but post batf ruling no new civilian developments over .500" groove. Darn, you can forget about that 800 nitro you were considering.
If you go with the S&W you can always have a custom mold made for the 515141 design but at about .502" diameter. Even with the shorter case Linebaugh you will have plenty of case volume for good velocity with smokeless powder. With black powder its hard telling what kind of velocity you might get. With the limited case volume is where you reverse directions with black powder. With an extra large case volume you would want to stay with a large grained powder like FG but with the smaller case volume to keep the pressure up you would go with a much smaller grain powder like FFFG or even possibly FFFFG to get comparably high velocity as the larger case.
One consideration will be rifling twist rate and black powder fouling. A faster twist rate combined with a more dense powder will equate to more fouling. Black powder fouling is one of the reasons original BP cartridges used the very minimum of twist rate to stabilize the intended bullet length.
A faster twist rate gives more surface area for fouling to build on.
A good example in cartridge history is the 30-30 and the 32 special. Though basically the same cartridge shooting the same bullet weight the 30-30 used a 1-10" twist while the 32 special used a 1-16" twist. The reason for the different twist was powder type to be used. At the time of development not everyone was ready to accept smokeless powder for loading ammo. The 32 special was for the stubborn older folks (like me) that didn't trust the new powder and wanted to keep using BP in loading their ammo. You can still load BP in both but the faster twist of the 30-30 will foul more quickly and to a greater degree than the 32.