I had trouble with all 250 grain bullet weights, getting accuracy that I was satisfied with for hunting.
I tried Hornady, Speer and Sierra type bullets.
You don't mention the twist rate or velocities so it's hard to give an opinion on your issue.
The rifle I used was a Winchester Mod 70 with a 23 in ER Shaw bbl, with a 1-12 twist rate.
I used Varget, IMR3031 and W748 and after a half dozen attempts with each of the above makers bullets gave up, after the best groups I could get were just around 3 inches at 100yds.
A friend suggested that I switch to 225 grain bullets with flat bases.
I bought a couple of 100ct Hornady and Speer cup and core offerings and my first load of IMR3031, 52.0grains went into 2 inches with either bullet.
I finally ended up increasing the load to 55.0grains of IMR3031 over CCI250 primers until I was getting just over 2600fps and the groups shrank to around 1.5 inches at 100 and maintained the 1.5moa out to 200yds, which is as far as my records show.
My records also show a couple of loads of Varget out to 200yds, the final ''best'' consistent groups were just over 2 moa, which would have been fine for most hunting I do.
I didn't find much if any difference between the Hornady and Speer as far as accuracy was concerned. They're both proven good performers on game.
Most people shooting the 338 and 35 cal cartridges really can't handle the recoil generated by heavier bullets. Not saying that's an issue with you.
So, they tend to opt for the lightest game bullets available for their loads, right down to the mid 180s grain weight. Why bother???? Go with a cartridge/rifle combo you can tolerate.
The 35 Whelan is a great cartridge and when loaded to its full potential, it's capable of taking any game animal I've hunted in North America ethically and cleanly if the shooter does their part.
My rifle was satisfactory for the ranges and type of hunting I do. However, the bbl was definitely not ''match quality" and I believe the two moa and 1.5moa group averages were about the best that could be wrung out of them.
At the time, I didn't need more and it was already obvious to me that the 338 bore cartridges were more attractive as I already had a couple of other rifles chambered for them and there was a much larger selection of components available for them.
No flies on the 35 Whelan and if it were the only cartridge available to me, I wouldn't feel the least bit under or over gunned.