Before this degrades into a mega-argument, let's back up and look at the OP's load data.
To wit:
"6 Grains of Unique/158 grain SWCHP."
A pretty mild .357 load. I've used it with cast bullets. Nice and accurate, with more authority than a +P .38 without overstating the case. It's nowhere near maximum .357 Magnum pressures.
6 Grains of Unique with the same bullet in a .38 Special case will drive pressures up...no question...but they still wouldn't hit SAAMI maximum .357 Magnum pressures.
Hot-loading plentiful .38 Special brass back when .357 brass was less prolific was pretty common, as long as the handloader understood the case capacity/pressure issue and reduced his powder charge to compensate.
As CraigC noted, .38 Special brass will take it. Other than the length, .38 brass is identical to .357 brass, with only the slight variations from one manufacturer to another...which isn't enough to make a practical difference. .38-44 brass differed only in the headstamp, and that was in order to identify it.
One does have to use a system to identify the heavily loaded .38 Ammunition to prevent it being fired in .38 Special revolvers...especially in small or medium-framed .38 revolvers...but that's about it. A dab of Sharpie marker on the rims, or designating one headstamp for that lot and no other is the usual method. Storing in clearly-marked boxes and leaving the .38 revolvers at home is another good one. Personally, I'd prefer all three because our old friend Murphy is alive, well, and active...and he never sleeps.