I bought heavy, gas checked cast bullets designed for a 357 from several sources. I believe GT Bullets has them. The bullets that I bought were sized either .359 or .360" (don't remember which but the suppliers had a range so sizes available).

It has been a while since I bought them but I found a couple of sources by Googling something like "hard cast gas checked bullets".

You might try some wide nose bullets. They are effective at short ranges.

I paper patched some 0.430" bullets to 0.439" for two rifles that required that bullet size.

The one thing to ask for is unlubercated bullets. If not available, remove the lub as that will cause the paper patch to adhere to the bullet.