Beretta 92FS, 1:32" barrel, and 124gr bullets?

I shoot a Beretta 92 a lot better than I do a 1911.  I just had a 1:32" KKM 9mm barrel installed in one of my Beretta 92FS pistols.  What has been recommended to me is 115gr bullets and either VV N340 or AA#7 powder.  I do have some of them in stock, but I have a much larger quantity of 125gr HAP and 125gr cast Lead bullets.  

Looking at posts by others, one was to the effect that the writer got really good results with 124gr Speer Lawman factory ammo in a 1:32" barrel.  

I'm looking for handload suggestions that others have found work in the Beretta with such a barrel and 125gr bullets.

I wouldn't use the .356 125gr HAP bullet. I tried it in my 952-2 and the slightly oversize bullet didn't like my tight barrel. I suspect your new KKM will not like it either. My 38 super however loves them.