I think the 178 Stone Hammer would be excellent in the 358 Win. Don't need to be concerned with high BC with the range of that cartridge. It will perform a lot better than the 220 TTSX in my opinion.
The Tikka is quite a bit better quality if you can swing the price difference. The .270 has been around for 100 years and it is still a very viable cartridge, able to kill pretty much anything in NA. Suggest getting a rifle model with a threaded muzzle. Leaves the option for adding a...
@44hunter45 nailed it along with what you said about the carpet on the bench. Hot brass on nylon carpet. Nylon brass catchers for AR's will do the same thing unless the brass can quickly fall out the bottom.