My friend and his son have a couple od Browning BLRs in 358 Win.
As you've already been informed, these rifles are chambered for modern high power rifle rounds operating at the upper end of the pressure ranges you see in the CIP/SAAMI tables. The actions are built to operate at those pressures - they aren't downgraded for low pressure older cartridges (which the 358 Winchester isn't in the first place). So if it is in the reloading manuals, it should be safe in any generic rifle of any kind factory chambered to 358 Winchester.
I loved my Leeper-built custom 358 Win BLR (wanted one in the time Browning wasn't making them). Then my wife fell in love with it and simply declared it was hers for life... so I think I need one of the new takedown versions...
Anyways, I think the Barnes TTSX, 200 grain version, is the best all round 358 Winchester load. The 180 grain version shoots marginally faster, but the higher BC of the 200 grainer overcomes the slower start once you start to get out to longer ranges anyways.
Looking at the loading data I got from Ramshot, I am using 47.0 grains of X-Terminator with a Federal Primer in Winchester brass with the Barnes 200 gr TTSX BT. It chronos at just over 2600 fps, and I think is about the maximum recommended load for that bullet and that powder in the 358 Win.
Going from memory, you end up with a point blank range of about 300 yards, about 18" low at 400 yards with about 1600 ft/lbs of remaining energy. Pretty much in the ball park of what you'd get out of a 30/06 with a 200 grain bullet over the same distance. In other words, hardly a mere "close range bush cartridge".
The wife neither knows nor cares anything about the numbers and ballistics. What she knows is every elk, moose, and mule deer she's pointed it at has pretty much gone down at the shot. And besides, she thinks it is really cool to hunt gophers with it all summer using 158 gr SWC lead bullets pushed by a few grains of Red Dot to about 950 fps... and those loads don't break the bank.