Can you use what amount to JHP, but with rubber or plastic plugs in the noses, until they hit the target? The plugs then enable expansion.
How do your laws read? No HP's, or no expanding bullets? That is an important distinction.
Failing any expanders, I'd go for Plus P lead semiwadcutter .38 ammo indoors, and .357 JSP outdoors, especially in the wild. I think the latter will kill a bear, if you hit him right. I know of one polar bear killed with .38 lead HP, and one killed with a 158 grain .357 JHP. You can't use these, but you'd have better penetration with a softpoint, and that's what mainly counts on bear, or deer, if that may be a factor. I think you're in a certain NE US state where cougars aren't a threat, but big dogs may be.
That .357 softponit will also do a number on people shooting at you from within a car.
If you CAN use HP's with the nose plugged, look at Hornady's Critical Defense ammo, if sold there. Federal also has a nose plug round, but I can't recall the name at the moment. Someone will probably tell us. They claim it's very effective.
Austria now allows some JHP use, by members of gun clubs. Maybe New Jersey will follow suit, if enough NJ shooters raise Cain, and Able, too.
Placement is the principal factor in stopping/killing power. Even military ammo works pretty well. I have that via someone I know who shot nine men in Iraq with 9mm's. He said they usually worked well, if well placed. He also said that if he hadn't had a pistol, he'd be dead now, himself.
Lone Star