You can get 200 gr .375 bullets, they are made for the 375 Winchester.
You can get ~ 150gr bullets in .358 caliber, they are designed for handgun cartridges.
Do you think a max loaded 158 gr Gold Dot would hold?
What about 125 grain?
I don't think so.
We need .358 Cal 150-180 grain heavy jacket aluminum core bullets or lead core.
Sectional density should be below .20
Penetration should be no more then 12 inches.
Velocity should be 3400 fps.
Think Magnum Varmint.