As Bill said, the .357 Herrett was designed to do just that. So, I would use it with confidence.
Now, as to your choice of bullets... That's a whole 'nuther horse race. Not to be obtuse, but why are you using flat-point bullets? In the single-shot, that's just a needless loss of ballistic coefficient. There's no reason not to use pointed (or round nose)bullets,,,,,,, except one: a long throat.
My Herrett barrel has a chamber with almost a half-inch leade, or throat, from the end of the case neck to the origin of the rifling. I can get close to the rifling with 180gr RN bullets, but not with the spitzers, and still have anything left in the case neck. Luckily, it will shoot almost as well with a bit (.250-.300") of jump as it does with the RN bullets up close to the rifling. I just settled on a 180gr (190gr checked & lubed) RN cast bullet. Contender chambering is well known for this. Kinda' like Weatherby.
If you go much over 200gr, you begin to loose too much velocity. At least from my point of view. I'd try loads with the 180 RN and some spitzers. Also try out the 200gr bullets of both types. By juggling seating depth and powder charges around a bit, I'm sure you will find something you like... Good Luck!!!