Do not put 357 Mag loads in 38 Special cases unless you seat the bullet out to 357 Magnum COL. Otherwise, you will be increasing pressure by lighting the powder up in a tighter space under the bullet.
Regarding the variation in published data, notice what the test gun was. Hodgdon is reporting a load fired in the SAAMI 7.710" Velocity and Pressure (V&P) test barrel, which is a closed-throat barrel used to mimic a single-shot handgun. Sierra is using the SAAMI 5.631" V&P barrel, which has a 0.008" vent at 1.623 inches from the breech to mimic a revolver barrel/cylinder gap, which does drop some pressure. Additionally, the Sierra bullet is a little shorter than the Hornady XTP, which also lowers pressure where the COL and all else are the same.
So, there are variables here. None will take you over 357 Magnum pressures, though. I think my approach would be to start with Hodgdon's load and look at velocity and see if it is satisfactory. If so, just stop there. Your 6-inch 357 Mag revolver barrel, if all its other dimensions and your chamber dimensions matched the vented SAAMI V&P barrel, it would be expected to take a cartridge that produces 940 fps in that V&P barrel up to 1010 fps. That would be so if you had 38 Special chambers. Yours are longer and will drop pressure more, so you are going to need more powder to get there than a 38 Special revolver of otherwise-matching dimensions would. BTW, that number is an average of ten shots measured with an optical chronograph whose midpoint between screens is 15 feet from the muzzle. See what the 5.3-grain load does over a chronograph with that spacing from your gun. If your fastest chamber still has it under 1010 fps, you can creep it up toward the heavier published loads. I just wouldn’t go over 1010 fps (average twelve shots since you have a six-gun) if you want to be at +P pressures.