I use Hornady 180gr SST's over 67gr of AA4350, Fed 215M primers, & Remington cases. Best so far 0.50" group at 100yds. 3 shot 1.25" group at 300yds. Rifle Weatherby Synthetic Vanguard VGD2. I have other bullet mfg's I was going to try but with results like these I don't think that's necessary at the moment. The 300 mag series of rifles (Weatherby, Winchester etc) were designed to work best with the 180gr bullet. Not saying that others are not good choices but that was the original idea.
Obvious question but have you verified that all screws etc are tight, barrel free floated, crown not damaged, etc, etc? How much was it shot in the past if known? It may need a scrub with something like JB Non Embedding Bore Cleaning Compound. Brownells has it.
Don't forget Weatherby rifles have a bit more free bore.
Memory's a little rusty here but I think the excessive "free bore" was more to do with the earlier FN and later JP Saur mfg Weatherby's before Howa took over production. Current free bore is .361 for 300Wby. Chime in if I'm incorrect.
Here is a quote from Shilen Rifles Inc " Weatherby rifles come with about 3/8ths of an inch of "free-bore" in them to help compensate for the high pressure the factory ammunition develops. If you intend to shoot factory ammunition in your rifle, then stay with a factory length throat as shortening the throat will probably show little or no increase in accuracy and may even prove detrimental. In fact, in Weatherby cartridges, this free-bore is necessary to avoid pressure problems when using factory ammunition" rifles.
If you seat the bullet too far out the neck tension may not be enough. Most people I have talked to that own Weatherby's seem to agree that seating a factory depths offers the most consistent accuracy. Don't forget though you have a hunting rifle and not a bench rest rifle so an inch to two inch isn't a bad group. The animal receiving the round isn't going to complain that your bullet hit 0.50" off where it was supposed to be (assuming your shooting within 200yds). As always you have to do your part.