The only 44 JSPs that had a reputation for shedding jackets were the old half-jacket bullets (usually Speer), which were a simple "cup and core" design. Simply put, all they did was squash lead into a simple half-jacket copper cup and crimp it into place lightly. Sometimes the jackets would stick in the bore when fired with light loads, and the core would break loose from inertia and travel on to the target. Meanwhile, the jacket in the bore became a bore obstruction, potentially causing disaster when a followup shot was fired. The only way to avoid this issue was to load these bullets a little hotter, to minimize the potential for the bullet sticking. Whatever bullet you choose, you will be in good shape if you simply follow the bullet manufacturers minimum velocity recommendations for the exact bullet you are using. Quite honestly, you can stick any bullet in the barrel if you don't follow these guidelines, and load them too "slow". If you want to load bullets for lower velocities, I'd stick with cast bullets. If you don't cast your own, these are a number of sources for good quality cast bullets. All you need to do is determine the performance level you need, and start contacting the makers. Since you're looking for penetration, a good quality flat nose cast bullet with a hardness of around 15 to 18 bhn should be all you need.
