Nothing wrong with either the original Winchester 95 nor the latest Japanese iteration.  Just don't expect the same slick handling you have experienced with your Krag.  Winchester also made their 1885 Single Shot in 30-40. Originals are very pricey.  Remington made the No. 3 (Hepburn) in 30-40.  Very rare and mid-to-high 4 figures in front of the decimal.  Remington also advertised their No. 5 Rolling Block, but I have never seen one.  Remington also made their Lee bolt action in 30-40.  Those are also relatively rare.  I have a Uberti "Winchester" high wall in 30-40.  It is a modern reproduction of the original Winchester 1885 rifle, made of modern steel with a bushed firing pin.  If you ever shot an original high wall, you will soon realize that the Uberti is not the real thing.  But it is close enough, safe and affordable.  Lots cheaper and easier to find than any of the originals.  I would recommend the Uberti, but that buttstock will need replacement.  Recoil hurts!   There was also a Ruger #3, but most of those have disappeared from the used gun racks.  You might find the Ruger or the Japanese 95 in the $400 to $600 range.  All the rest will cost more.

Lee Navy rifles were 6MM cal

Other than being made by Winchester, the Lee Navy had nothing in common with the John Browning-designed 1895 Winchester.  Total production was 20,000 . It fired a rimless cartridge with a steel-jacketed round nosed bullet.  Some of the first bullets weighed 135 grains, later changed to 112 grains. Barrels had a 1: 6 1/2 " twist. The small bore (.243), steel bullet jackets, corrosive primers and very-hot burning double-base powders made for short barrel life. Steel bullet jackets were changed to cupro-nickle, but that did not help.  MV was about 2500 to 2600.  Lots of CN fouling.  The cartridge case was smaller in diameter than the contemporary Mauser rimless cases. Case length was 61 mm, with a 30-06 case being 63 mm.  Only similar case is the 220 Swift.  Turning the rims off Swift cases makes usable Lee Navy cases.  If you are after accuracy, they can be swaged from 30-06 cases.  It is a major job.

The magazine was nothing like the 1895 Winchester.  Cartridges were inserted with the clip, something like the early Mannlicher rifles. The original clips can still be found.

I tried to buy a shootable Lee Navy in 2007.  Went to the big Reno show with $2500 in my pocket.  I found the only one at the show, but the seller wanted $4500.  $4000 seemed to be the asking price at auction. Maybe lower now.  Then I heard of a guy who restored one getting killed when the striker blew out.  Price + risk took me out of the Lee Navy game.  In 2008, one of the rifles from the Winchester test room was offered by one of the big auction places.  It went for $4200.

The Navy & Marines abandoned the Straight-Pull Lee about 1904.  Main problem was the 800-yard effective range of the cartridge. Contemporary military cartridges had effective ranges of 1500 to 2000 yards. 100 years later our troops have the same problem.

Krags were issued to replace the Lees.

Some Gatling Guns and Colt (Potato Digger) Machine Guns were built in .30-40 (.30 U.S. Army), as well as, 6mm USN.  Tripod and carriage mounted Colt Machine Guns in 6mm were used by our Marines in Cuba and the Phillipines in 1898 and in Somoa and China around 1900.

The Manual for "The United States Navy Rifle, Calibre 6 Millimetres, Model 1895.", (1896 printing) is reproduced.  It has a nice fold-out of the Navy rifle.

We marched almost that well when I was in the Navy 1960-65.  Apparently there are some re-inactors who get into the spirit.  It is possible ($$) to purchase reproductions of all the pouches, belts, etc.  Also parts and new production stocks for the Lee Navy. 

But there were problems with the striker.  The Navy or Marines obtained modified bolts somewhere along the line.  I have seen rifles described as having a modified bolt.  Reading about the guy who had a striker penetrate his eye and then his brain took all the fun out of the Lee Navy game.

Well, as is usually the case... there is a plethora of people on this site with a wealth of incredible knowledge!

I only meant that I thought the magazine looked similar in shape to the 1895 Winchester.  I didn't have much time to get a good look, just a quick snap of my camera.  And they didn't provide much info either, especially about ammo (something they didn't mention for any of the rifles except the mini-ball for the Springfield percussion of the Civil War).  I just assumed it was 30-40.  I had no idea about the dangers involved with this weapon.

Interestingly enough, they had tons of Garands and 1903's on display, but only one Krag (an 1896, with an 1899 rear sight) and one Trapdoor (an 1886), and no carbine examples of either!