A 340 always seem to be "250grain" cartridge for me. My normal go-to test load is 86grs 7828ssc in WBY brass with a Fed 215 primer. The 250 Nosler/Swift/TSX will do wonderfully in it.

That said, my first ever Weatherby Mark V was a .340Laser. I bought a few 210gr factory loads in it, one .40cal ragged hole. It would throw them into one hole as long as you could stand to sit behind it. I saved up and bought a big pile of that same ammo, same lot number.