I would strongly recommend against using Ackley cartridges in anything but a bolt gun. If it is chambered tight enough to support the case properly you won't be able to close the lever.
Also keep in mind the barrel would have to be set back a turn to headspace properly. I am not familiar enough with the 1895 to say if that would work or not, but how is the forend attached? If it's screwed to the barrel or on a hanger it's not going to line up any more.
Now, I don't know that he does 338 but Jesse Ocumpah (sp?) does a good 35 cal. rebore, and making it a 35 Whelen would likely work very well and not run into headspace issues. He gets about $225 for that, cheaper than a good barrel blank.