I personally do not believe that you can run a 500 gr .500 caliber bullet in the 500 S&W to 2000+. There is not enough case capacity, nor suitable powder to achieve that velocity, in that case. 400 gr, Yes.........
And here is why I have that opinion;
The 50 B&M Super Short is very near identical to the 500 S&W cartridge. 50 B&M SS is a cut/trimmed WSM case to 1.650 and the S&W case is 1.625, so the 50 B&M case is slightly bigger, 69 gr of water capacity, S&W at 65 gr. This is important in the following information.
50 B&M SS is designed for the WSSM M70 action. And can handle 65000 PSI without issue. The rifles have 16 inch barrels. In .500 caliber, there is a lot of interior burning cubic inches. This makes .500 pretty efficient using appropriate powders. In my research here these cases have a very narrow window of the type powder that is efficient. In the beginning WW 296 was top end, until I tried LilGun. Lilgun edges out WW 296 by just a smidge, with slightly more velocity at lower pressures. But just by a smidge. Going with a slower powder on the scale you run into case capacity before reaching optimum velocity. Going faster you reach Pressure limits before getting to optimum velocity. A very narrow window.
I also have the capability of running Pressures here as well. I tested the 500 gr Hornady FN Soft many years ago in the 50 B&M SS. I was able to get 1777 fps with 39/LilGun at 64500 PSI. 40/WW 296 ran 1715 fps at 60000 PSI, I did not go any further with it, could have probably made 1750 fps with WW 296 without going over 65000 PSI, but I did not see a point in it.
To claim 2000-2150 fps with a 500 gr .500 caliber in the S&W Case, which is smaller than the B&M just does not add up to me, even at 22 inch barrel. I am pretty sure there is no way you would gain that much velocity in 6 inches extra barrel. Remember inside Cubic Inch Burn? You don't gain 40-50 fps per inch with these powders. If you gain anything at all, which is also a little doubtful, then it would be between 10 fps and 20 fps per inch at the most.
400 gr bullets we can get 2050 to almost 2100 fps in the 16 inch B&M version without going over 65000 PSI. You might get to 2150 with a 400 with the 22 inches....... or close, Maybe..........
Now, can the Big Horn handle 65000 PSI? I really don't know, but honestly I would suspect it might. Reason being, I had contact with the owner of Big Horn before his lever action was ready for market, they were still design and making....... Very nice fellow, and seemed to be very serious about the Big Horn being what they claim it to be today, and I do not doubt it is very Top Of The Line. I suspect he built a lot of strength in the action. He was very interested in my 50 B&M Alaskan, also a lever cartridge based off the .510 Alaskan, just squeezed down to .500 caliber. This cartridge can be done on the 1895 Marlins and the Winchester/Browning M71s. I can tell you this for sure on these guns, the 1895 Marlin can handle 45000 PSI before running into issues, and I think you can run 50000 PSI or so in the M71s. The Alaskan case is much bigger, 2.1 inches and 85 gr water capacity.
Regardless of the above, it is really a moot point. You don't need a 500 gr .500 caliber bullet to conduct business on DG in the field. If you use proper designed bullet tech, then you can rule the world. I needed proper bullet tech for all the B&M cartridges, but in particular the various .500 caliber cartridges. At the time I started this, there was only S&W Handgun bullets available. I needed something much more substantial to do things I wanted to do, so we went to work.
For buffalo +, I really like for a bullet to start out at 2100 +. I was coming up just a little short with 400s in the 16 inch 50BM SS..... I dropped to 375 gr for the Solids, in both CEB and North Fork. CEB made a Raptor from the 375 Solid at 335 gr. North Fork made a matching 375 gr Expanding CPS for me. These bullets would prove their worth in the field, and turn this cartridge into a serious hammer, even with its tiny size compared to anything else...... overall 36 inches total, and 6.25 lbs without scope. 375 Solids from 2150-2200 fps running a modest 60000-62000 PSI, same with the 375 North Fork Expanding CPS and we could bump up the 335 Raptor to 2225-2250 fps.
In 2012 I took the entire family Down Under to do some shooting with Paul Truccolo. My best friend Sam Rose was along as well, he was testing some new CEB bullets for his 500 NE guns. My Son Matthew had his 50 B&M Super Short, loaded with CEBs and North Forks. Mark David had his 475 B&M Super Short loaded also with CEB and North Forks designed for his 475 SS at .474 caliber, they came in at 350 and 375 as well. Sam was shooting a new 475 Raptor and 510 Solid from CEB in his 500 NE.
The boys really put on a show. Sam and Paul both watched intensily as Matthew worked the little 50 SS with ease, both made the comments that it was just as effective on buffalo as Sam's 500 NE! They said, not me, but it was getting the buffalo's attention in a very serious way. None of the Solids were recovered, they all burned .500 caliber holes through and through. Mostly broadside and very angled shots, I don't know of any rear to front or front to rear that the boys did. Some Raptor bases were recovered from broadside shots.......
This is a 325 Raptor .474 from the 475 Super Short;
Matthew slammed this big body tank of a bull with his 50 Super Short..... two North Fork Expanding CPS, angled shots...... both recovered see below, and 1 375 North Fork Solid from severe angle forward that exited..........
Matthew shot 20 or so buffalo on this trip with the 50 SS, it was a solid hammer on buffalo without any doubt at all. This was observed by 3 very experienced individuals. In addition, the .474 caliber SS did just as good. 20 or so buffalo for Mark David, and he never came up "Short" at all either. Mark David would go on later to take elephant with his 475 B&M SS with a 350 CEB Solid at 2200 fps, side brain at 10 steps, done and over, and exited far side..........
So can the Big Horn Armory in 500 S&W stand the test of Big Dangerous Game? Oh yes without any doubt, but you need to use proper bullet tech. As far as that goes, it don't matter if you use a 500 NE, you still have to have proper bullet tech! If you do not have the right bullets, you will fail regardless of the cartridge or rifle.
I have taken the notion several times that I wanted a Big Horn 500 S&W...... but with the 50 Super Short in the Bolt gun, and my own 50 B&M Alaskan lever guns, I can't really justify it, and it won't do anything that what I have already won't do........ But they are super nice and I believe they are top notch first class firearms and would be damn hard to beat.......... Well done Big Horn.