My only .35 Caliber hunting arm was a Marlin 336 in .35 Rem. For this, I used a 200 grain soft point, usually by Remington or Winchester and either would put a whitetail down in short order.
I stopped using hand loads in this caliber as no matter how I adjusted the dies, I suffered occasional failures to fire. The lack of a shoulder on this cartridge can be problematic.

I've had no issues with factory loads. BTW, I think your .358 Win. is a perfect woods cartridge with some range if you need it.