Sheldon, as much as I would like to say that you should go with the .340 Wby because of the added power, but I think a 24" tube is a little short for it so I would just stick with the .338 Win. I sounds like you are doing pretty well with it as it is. You may want to invest in another rifle.
If you already have .338 Win mag and wish to sample the "wild side" just purchase a box of Federal Premium HIGH Energy rounds. These
factory hot pills drive 250gr Nosler Part. out of your 338 Win Mag at .340 WB. I had them on last Elk hunt however down side was them Elks got word of potential and hide out