Darkman...........You are talking one of my all time favorite cartridges. Not sure where you heard that BS about hangfires specific to Weatherby cartridges, I can assure you it's not true. Use good magnum primers and follow the loading manuals and I'm sure you will find a good load. What rifle is your 340 in, a Mark V or a custom chambering on another action?
The 340 is as easy to load for as any other bottle neck rifle cartridge and requires no special treatment at all. I have had good success with Alliant RL 25, but your manuals will give a listing of suitable range powders. The manuals are very conservative due to custom chamberings not necessarily having the same length of leade as the Mark V, hence my previous question. Check your leade or if it is a Mark V just load to the maximum magazine length allowable. My previous Mark V would consistently cloverleaf 3 - 250 gn Nosler Parts at 100 mtrs if I was doing my part that day. The 338 Howa I chambered out to 340 wouldn't keep 3" at 100 mtrs and rechambering didn't improve it one bit. My current Win Supergrade is showing a lot of promise but I'm not done working with it yet. It is shooting 225s well under an inch but I haven't had a chance to try my 240 gn bonded boattails yet.
If you are desensitized enough, recoil wise, to shoot the 340 well you will learn to love it..........very few cartridges on this planet kill medium to large thin skinned game as well as a 340, right out past 500 mtrs. I have always said the 340 Weatherby is one of the killingest cartridges I have ever unleashed on NA game........of any size. It shoots like a 7 Mag and hits like a freight train.