First, your biggest problem is going to be finding a 357 handi. You will have to buy it used. H&R quit selling the 357 as a full rig for some reason. You can still buy the 357 mag barrel, but last I heard, they are currently out of stock.
Now, for your question. My max does shoot 357 mags and 38s extremely well, but oddly enough, very differently from the 357 max. I have a really difficult time switching back and forth from the max to the other two. I have asked this question of other max owners and all that I have talked to have just suggested shooting max shells all the time with lighter loads when desired. I haven't tried this yet, but intend to.
I am far from an expert, but these have been my findings in the 6 months or so that I have had this rifle.