I am the founder of Cast Performance Bullet co back when it started in Gardnerville Nevada. I and my partner later moved it to Riverton Wyoming.
As the founder, later ballistician and finally the CEO (Turned it over at the end of 1998) I have a great deal of experience with hunting handguns, what bullets work and how well, personal hunting kills in a fairly large number and I used to read letters and reports and talk to hunters by the literal thousands who had used the bullets we produced as well as a lot of bullets our competitors made too.
In my experience and in the experience of many hundreds of customers who killed big game with 357 Magnum handguns, if I were to recommend for those animals you named I would tell you that for any animal up to about 175 pounds and non-fragmenting soft point is fine and any LBT hard Cast bullet in the LFN or WFN is going to be superb. When you go up to the game animals of 250 pounds and up to elk and kudu size the bullet you want is the LBT 187 grain Wide Flat nose Gas-checked. In shooting these by the thousands in our tests against all other bullet we made and all others of different designs as well as about 15 other jacketed and solid copper bullets, the 187 grain LBT was equal to the very best in a few categories and superior in every other category.
Categories for the tests and the field reports were
#1 Accuracy,
#2 penetration,
#3 cavitation (meaning cubic inches of displacement of tissue. Also called "wound channel")
#4 Accuracy,
#5 trajectory and wind drift, and
#6 pressure and pressure curves.
I have not been involved with Cast Performance now for 17 years. So I have "no dog in the fight" now. That is important to know because when I recommend an LBT design in a cast bullet of 185 to 192 grains I have no "reward" if you do, and I am not hurt in any way if you don't. But I have personally killed several white tail deer, mule deer and antelope with 357 handguns and I have friends who have killed many more. I were to guess that number to be around 60. I have read letters and talked to at least 500 more hunters on the phone that have done it. If you throw in the 44 spl and mag shooters, the 41 mag shooters, the 45 shooters and the 454 Casull shooters that number would go up many many times.
So you can trust me when I say that a proper cast bullet of the LBT style is outstanding. I must say that a well fitted Keith bullet is very good too, and in fact one that fits your gun can come pretty close to the LBT style in the 6 categories, but if I am to recommend one above all others it's going to be the LBT hard cast bullet.
On light game a good hollow point will kill as well but when you judge over all in all 6 categories as an average, the LBT is still the best.