Snake Oil, for some reason the Martini-Henry (along with the Martini-Metford and Martini-Enfield) have been very commonly faked, and a lot of them have ended up in the USA as "bring-backs" from Afghanistan and other nearby places. I wouldn't be surprised if there are more Khyber fakes for sale in the US than there are genuine Martinis, so it definitely pays to exercise extreme caution in buying. Do let us know if you can get this seller to take this one back …
In Canada we are fortunate in having had a lot more genuine Martinis floating around, and relatively few fakes … but the supply seems to be drying up here also, and prices have certainoy been climbing.
Since the carbine was a diversion from the personna you had originally planned, I assume that a rifle would still be accceptable to you … perhaps even preferable. If so IMA, as suggested by Niederlander, may far and away be your best bet in the USA as long as you stick with one of the ones they describe as "Original British P-1871 Martini-Henry MkII Short Lever Rifle". Stay away from their Nepalese Gahendra and Francotte-type rifles … they are Nepalese made, and in any event not suitable for any British Empire impression you might decide to do. Similarly, although the "P-1885" Mk IV rifles are cheaper, they were never issued to any British Regular Army unit. their use having been limited primarily to the Indian Army, with some known issue to Volunteer units in the UK.
If I were ordering from IMA (though I wouldn't since I currently own three Martini-Henry rifles with Canadian military provenance) I would probably stick with a "cleaned and complete" rifle … even springing extra for the "hand select" option, if they still offer that … and, considering your intended use, the extra cost for a rifle with bayonet and scabbard is well worth it. (Finding a decent bayonet, with scabbard., separately will take time and effort, and cost at least that much, if not more, anyway.)
Just to keep your desire active, here is one of my rifles …